Alaa A . Abdallah | Aden University (original) (raw)

Papers by Alaa A . Abdallah

INTERNATIONAL JOURNAL OFMULTIDISCIPLINARY RESEARCHIN SCIENCE, ENGINEERING AND TECHNOLOGY, 2025

This paper investigates the properties of C^{hv}-mixed birecurrent Finsler spaces within the Cart... more This paper investigates the properties of C^{hv}-mixed birecurrent Finsler spaces within the Cartan sense. By employing specific methods. In this paper, we introduce Finsler space F_{n} who's the torsion tensor C^i_{jk} satisfies the birecurrent conditions with respect to the first and second kind of covariant derivatives in Cartan sense. Also, we study the relationship between Cartan's first curvature tensor S^i_{jkh} and h(hv)-torsion tensor C^i_{jk} in sense of Cartan.

Journal of Finsler Geometry and its Applications, 2024

This paper deals with space known as "generalized fifth recurrent Finsler space." The core idea c... more This paper deals with space known as "generalized fifth recurrent Finsler space." The core idea centers around a mathematical object called the" Inheritance Kulkarni-Nomizu product" which is applied to two Ricci tensors satisfy an inheritance property. We apply the inheritance property with Kulkarni - Nomizu product of two Ricci tensosrs by using Lie - derivative in generalized fifth recurrent Finsler space. In addition, we prove that the Lie - derivative of the inheritance Kulkarni - Nomizu product of K-Ricci tensor and H-Ricci tensor vanishes simultaneously.

J. Int. Acad. Phys. Sci., 2024

This study employs advanced tensor calculus techniques to investigate the properties of the tenso... more This study employs advanced tensor calculus techniques to investigate the properties of the tensorial derivative in generalized fifthorder recurrent Finsler spaces. By systematically analyzing the underlying geometric structure, we derive identities that provide new insights into the relationships between various tonsorial quantities. Our results demonstrate the effectiveness of these techniques in exploring complex geometric structures. This paper introduces a new identity connecting the tensors in generalized fifth recurrence Finsler space for Cartan's fourth curvature tensor in the sense of Berwald by using Liederivative. We prove that the Lie-derivative and the Berwald covariant derivative of the fifth order for some curvature and torsion tensors are commutative under certain conditions. We have shown the Liederivative for some tensors behave as fifth recurrent and we obtain various identities on Lie-derivative in GℬK − 5 RF_n

International Journal of Advanced Research in Science, Communication and Technology, 2024

This paper introduces a class of Finsler structures, termed hyper-generalized recurrent Finsler s... more This paper introduces a class of Finsler structures, termed hyper-generalized recurrent Finsler structures. These structures are defined by particular curvature tensors in conjunction with Berwald's covariant differentiation. This paper extends the theory of recurrent Finsler structures by introducing a new class of structures defined by specific curvature tensors and Berwald's covariant differentiation. The findings of this research contribute to a deeper understanding of the intricate interplay between curvature and recurrent properties in Finsler geometry.

International Journal of Advanced Research in Science, Communication and Technology, 2024

This paper introduces a Finsler space which Wely's curvature tensor WjkhiW_jkh^iWjkhi satisfies the trire... more This paper introduces a Finsler space which Wely's curvature tensor WjkhiW_jkh^iWjkhi satisfies the trirecurrence property in sense of Cartan. Further, we study the relations between the Wely's curvature tensor WjkhiW_jkh^iWjkhi , normal projective curvature tensor NjkhiN_jkh^iNjkhi and Berwald curvature tenser HjkhiH_jkh^iHjkhi.

International Journal of Mathematics and Statistics Invention, 2024

This paper has focuses on a specific class of Finsler spaces known as generalized birecurrent Fin... more This paper has focuses on a specific class of Finsler spaces known as generalized birecurrent Finsler space. By introducing a new geometric structure, we investigate the properties of these spaces and establish several theorems. Our results generalize previous work on birecurrent Finsler spaces and provide a deeper understanding of their geometry. In this paper, we introduced an extension of the generalized U −birecurrent Finsler spaces. i.e., we define a Finsler space F_n which the curvature tensor U^i_{jkh} satisfies the extension for generalized birecurrence property in sense of Cartan. Further, we get the relations among different curvature tensors in the main space.

EQUATIONS, Nov 13, 2023

In this study, by evaluating two mappings that do not both exhibit direct continuity features, fr... more In this study, by evaluating two mappings that do not both exhibit direct continuity features, fresh results were found supporting the uniqueness of the solutions in generalized spaces.

Journal of International Academy of Physical Sciences, 2024

This paper discusses the decomposition for curvature tensor KijkhK^i_{jkh}Kijkh in generalized recurrent ... more This paper discusses the decomposition for curvature tensor KijkhK^i_{jkh}Kijkh in generalized recurrent space of fourth order. We explore the decomposition tensors (X^i Ѱ_{jkh}) and (X_j Ѱ^i_{kh}) are generalized ℬ-quad-recurrent tensor under two decomposition forms. If the recurrence covariant tensors a_{lmns} and u_{lmns} have symmetry and skew-symmetric properties, then we get various identities belong to the main space. Moreover, new formula for Cartan's 4^th curvature tensor KijkhK^i_{jkh}Kijkh has been obtained under the decomposition.

International Journal of Advances in Applied Mathematics and Mechanics, 2024

This paper builds upon existing work on generalized BK−recurrent Finsler space. We define a new t... more This paper builds upon existing work on generalized BK−recurrent Finsler space. We define a new type of Finsler space that considers extension for the above mentioned space. In other words, we introduce a new class of Finsler spaces call "second generalized BK−recurrent Finsler space". Within these spaces, we prove that the tensor RihykR^i _{h} y_kRihyk is symmetric and exhibits the remarkable property of aligning perfectly with the h(v)−torsion tensor H^i _{hk}. Furthermore, we demonstrate that certain tensors exhibit generalized recurrent behavior under specific conditions. Also, we infer that K−Ricci tensor K -{jk} and R−Ricci tensor R _{jk} both are equal in the main space.

International Journal of Physics and Mathematics, 2024

This paper builds upon the Finsler space is known generalized BP - recurrent space. We use B - c... more This paper builds upon the Finsler space is known generalized BP - recurrent space. We use B - covariant derivative of higher order to find generaliztion for the above mentioned space. In particular, we apply B - to study the relations between various curvaturs tensors.

International Journal of Advanced Research in Science, Communication and Technology, 2024

In this paper, we study the necessary and sufficient conditions for these tensors H_{jkh}^i, H_{k... more In this paper, we study the necessary and sufficient conditions for these tensors H_{jkh}^i, H_{kh}^i, (H_{hk}-H_{kh}), H_{j}^i, H, K_{jkh}^i, K_{jk}, K_{j}, R_{jkh}^i, R_{jk} and R_{j} in generalized βH- trirecurrent with respect to Berwald connection.

International Journal of Research Publication and Reviews, 2024

In this paper, we introduce a Finsler space which Cartan’s third curvature tensor RjkhiR_{jkh}^iRjkhi sat... more In this paper, we introduce a Finsler space which Cartan’s third curvature tensor RjkhiR_{jkh}^iRjkhi satisfies the generalized birecurrence property by using the first and second kind of covariant derivatives simultaneously in Cartan sense. Further, we prove that some tensors are non-vanishing. Certain identities belong to main space have been studied.

International Journal of Advance and Applied Research, 2024

In this paper, we introduced a Finsler space which WijkhW^i_{jkh}Wijkh satisfies the birecurrence propert... more In this paper, we introduced a Finsler space which WijkhW^i_{jkh}Wijkh satisfies the birecurrence property in sense of Cartan. Further, if the directional derivative of covariant tensor field vanish, then the curvature tensor HijkhH^i_{jkh}Hijkh, associate tensor HjskhH_{jskh}Hjskh and Ricci tensor HjkH_{jk}Hjk are birecurrent in Affinely connected space.

The Scholar Journal for Sciences & Technology, 2024

The relations between various curvature tensors discussed by Finslerian geometrics. In this paper... more The relations between various curvature tensors discussed by Finslerian geometrics. In this paper, two theorems that clarify the relationship between P_{ijk}^h and R_{ijk}^h in generalized tri-recurrent space are discussed. Moreover, the behaviour of some tensors are tri-recurrent if R_{ijk}^h satisfies the generalized tri-recurrence property.

Journal of Finsler Geometry and its Applications, 2024

In the generalized Branciari space, this paper develops and reproves some conclusions from the li... more In the generalized Branciari space, this paper develops and reproves some conclusions from the literature.

International Advanced Research Journal in Science, Engineering and Technology, 2024

In this paper, we obtain the necessary and sufficient condition for W^i_{jkh}, N^i_{jkh} and H^i_... more In this paper, we obtain the necessary and sufficient condition for W^i_{jkh}, N^i_{jkh} and H^i_{jkh} to be recurrent and we get a relationship between them. The projection on indicatrix with respect to Cartan connection has been studied.

AIP Conference Proceedings, 2024

In this paper, we discuss the relationship between WijkhW^i _{jkh}Wijkh and PijkhP^i _{jkh}Pijkh in generalized r... more In this paper, we discuss the relationship between WijkhW^i _{jkh}Wijkh and PijkhP^i _{jkh}Pijkh in generalized recurrent and birecurrent Finsler space. Further, we obtain the condition for WijkhW^i _{jkh}Wijkh that is a generalized recurrent and birecurrent tensor. Additionally, several corollaries have been obtained.

Int. Jr. of Contemp. Res. in Multi., 2024

Deviating from the traditional framework to prove the existence and uniqueness of a fixed point a... more Deviating from the traditional framework to prove the existence and uniqueness of a fixed point and replacing the fixed number in the Banach contraction principle with a function that has its conditions is one of the most difficult challenges facing studies concerned with the fixed point, which researchers took on recently. Success in such studies has a wide applied impact in many areas of mathematics, reflecting positively on various applied sciences. In this study, we establish new fixed point theorems for contractive mapping in a complete metric space using some helping functions via Caristitype.

International Journal of Research Publication and Reviews, 2024

A basic version of the Hardy-Rogers fixed point theorem is presented in this study.

Journal of Drug Designing and Bioinformatics, 2023

In this paper, Cauchy-Schwarz inequality on n-inner product spaces is reproved, and notions of or... more In this paper, Cauchy-Schwarz inequality on n-inner product spaces is reproved, and notions of orthogonality on n-normed spaces are introduced. This is the first approach to orthogonality types in such spaces.

INTERNATIONAL JOURNAL OFMULTIDISCIPLINARY RESEARCHIN SCIENCE, ENGINEERING AND TECHNOLOGY, 2025

This paper investigates the properties of C^{hv}-mixed birecurrent Finsler spaces within the Cart... more This paper investigates the properties of C^{hv}-mixed birecurrent Finsler spaces within the Cartan sense. By employing specific methods. In this paper, we introduce Finsler space F_{n} who's the torsion tensor C^i_{jk} satisfies the birecurrent conditions with respect to the first and second kind of covariant derivatives in Cartan sense. Also, we study the relationship between Cartan's first curvature tensor S^i_{jkh} and h(hv)-torsion tensor C^i_{jk} in sense of Cartan.

Journal of Finsler Geometry and its Applications, 2024

This paper deals with space known as "generalized fifth recurrent Finsler space." The core idea c... more This paper deals with space known as "generalized fifth recurrent Finsler space." The core idea centers around a mathematical object called the" Inheritance Kulkarni-Nomizu product" which is applied to two Ricci tensors satisfy an inheritance property. We apply the inheritance property with Kulkarni - Nomizu product of two Ricci tensosrs by using Lie - derivative in generalized fifth recurrent Finsler space. In addition, we prove that the Lie - derivative of the inheritance Kulkarni - Nomizu product of K-Ricci tensor and H-Ricci tensor vanishes simultaneously.

J. Int. Acad. Phys. Sci., 2024

This study employs advanced tensor calculus techniques to investigate the properties of the tenso... more This study employs advanced tensor calculus techniques to investigate the properties of the tensorial derivative in generalized fifthorder recurrent Finsler spaces. By systematically analyzing the underlying geometric structure, we derive identities that provide new insights into the relationships between various tonsorial quantities. Our results demonstrate the effectiveness of these techniques in exploring complex geometric structures. This paper introduces a new identity connecting the tensors in generalized fifth recurrence Finsler space for Cartan's fourth curvature tensor in the sense of Berwald by using Liederivative. We prove that the Lie-derivative and the Berwald covariant derivative of the fifth order for some curvature and torsion tensors are commutative under certain conditions. We have shown the Liederivative for some tensors behave as fifth recurrent and we obtain various identities on Lie-derivative in GℬK − 5 RF_n

International Journal of Advanced Research in Science, Communication and Technology, 2024

This paper introduces a class of Finsler structures, termed hyper-generalized recurrent Finsler s... more This paper introduces a class of Finsler structures, termed hyper-generalized recurrent Finsler structures. These structures are defined by particular curvature tensors in conjunction with Berwald's covariant differentiation. This paper extends the theory of recurrent Finsler structures by introducing a new class of structures defined by specific curvature tensors and Berwald's covariant differentiation. The findings of this research contribute to a deeper understanding of the intricate interplay between curvature and recurrent properties in Finsler geometry.

International Journal of Advanced Research in Science, Communication and Technology, 2024

This paper introduces a Finsler space which Wely's curvature tensor WjkhiW_jkh^iWjkhi satisfies the trire... more This paper introduces a Finsler space which Wely's curvature tensor WjkhiW_jkh^iWjkhi satisfies the trirecurrence property in sense of Cartan. Further, we study the relations between the Wely's curvature tensor WjkhiW_jkh^iWjkhi , normal projective curvature tensor NjkhiN_jkh^iNjkhi and Berwald curvature tenser HjkhiH_jkh^iHjkhi.

International Journal of Mathematics and Statistics Invention, 2024

This paper has focuses on a specific class of Finsler spaces known as generalized birecurrent Fin... more This paper has focuses on a specific class of Finsler spaces known as generalized birecurrent Finsler space. By introducing a new geometric structure, we investigate the properties of these spaces and establish several theorems. Our results generalize previous work on birecurrent Finsler spaces and provide a deeper understanding of their geometry. In this paper, we introduced an extension of the generalized U −birecurrent Finsler spaces. i.e., we define a Finsler space F_n which the curvature tensor U^i_{jkh} satisfies the extension for generalized birecurrence property in sense of Cartan. Further, we get the relations among different curvature tensors in the main space.

EQUATIONS, Nov 13, 2023

In this study, by evaluating two mappings that do not both exhibit direct continuity features, fr... more In this study, by evaluating two mappings that do not both exhibit direct continuity features, fresh results were found supporting the uniqueness of the solutions in generalized spaces.

Journal of International Academy of Physical Sciences, 2024

This paper discusses the decomposition for curvature tensor KijkhK^i_{jkh}Kijkh in generalized recurrent ... more This paper discusses the decomposition for curvature tensor KijkhK^i_{jkh}Kijkh in generalized recurrent space of fourth order. We explore the decomposition tensors (X^i Ѱ_{jkh}) and (X_j Ѱ^i_{kh}) are generalized ℬ-quad-recurrent tensor under two decomposition forms. If the recurrence covariant tensors a_{lmns} and u_{lmns} have symmetry and skew-symmetric properties, then we get various identities belong to the main space. Moreover, new formula for Cartan's 4^th curvature tensor KijkhK^i_{jkh}Kijkh has been obtained under the decomposition.

International Journal of Advances in Applied Mathematics and Mechanics, 2024

This paper builds upon existing work on generalized BK−recurrent Finsler space. We define a new t... more This paper builds upon existing work on generalized BK−recurrent Finsler space. We define a new type of Finsler space that considers extension for the above mentioned space. In other words, we introduce a new class of Finsler spaces call "second generalized BK−recurrent Finsler space". Within these spaces, we prove that the tensor RihykR^i _{h} y_kRihyk is symmetric and exhibits the remarkable property of aligning perfectly with the h(v)−torsion tensor H^i _{hk}. Furthermore, we demonstrate that certain tensors exhibit generalized recurrent behavior under specific conditions. Also, we infer that K−Ricci tensor K -{jk} and R−Ricci tensor R _{jk} both are equal in the main space.

International Journal of Physics and Mathematics, 2024

This paper builds upon the Finsler space is known generalized BP - recurrent space. We use B - c... more This paper builds upon the Finsler space is known generalized BP - recurrent space. We use B - covariant derivative of higher order to find generaliztion for the above mentioned space. In particular, we apply B - to study the relations between various curvaturs tensors.

International Journal of Advanced Research in Science, Communication and Technology, 2024

In this paper, we study the necessary and sufficient conditions for these tensors H_{jkh}^i, H_{k... more In this paper, we study the necessary and sufficient conditions for these tensors H_{jkh}^i, H_{kh}^i, (H_{hk}-H_{kh}), H_{j}^i, H, K_{jkh}^i, K_{jk}, K_{j}, R_{jkh}^i, R_{jk} and R_{j} in generalized βH- trirecurrent with respect to Berwald connection.

International Journal of Research Publication and Reviews, 2024

In this paper, we introduce a Finsler space which Cartan’s third curvature tensor RjkhiR_{jkh}^iRjkhi sat... more In this paper, we introduce a Finsler space which Cartan’s third curvature tensor RjkhiR_{jkh}^iRjkhi satisfies the generalized birecurrence property by using the first and second kind of covariant derivatives simultaneously in Cartan sense. Further, we prove that some tensors are non-vanishing. Certain identities belong to main space have been studied.

International Journal of Advance and Applied Research, 2024

In this paper, we introduced a Finsler space which WijkhW^i_{jkh}Wijkh satisfies the birecurrence propert... more In this paper, we introduced a Finsler space which WijkhW^i_{jkh}Wijkh satisfies the birecurrence property in sense of Cartan. Further, if the directional derivative of covariant tensor field vanish, then the curvature tensor HijkhH^i_{jkh}Hijkh, associate tensor HjskhH_{jskh}Hjskh and Ricci tensor HjkH_{jk}Hjk are birecurrent in Affinely connected space.

The Scholar Journal for Sciences & Technology, 2024

The relations between various curvature tensors discussed by Finslerian geometrics. In this paper... more The relations between various curvature tensors discussed by Finslerian geometrics. In this paper, two theorems that clarify the relationship between P_{ijk}^h and R_{ijk}^h in generalized tri-recurrent space are discussed. Moreover, the behaviour of some tensors are tri-recurrent if R_{ijk}^h satisfies the generalized tri-recurrence property.

Journal of Finsler Geometry and its Applications, 2024

In the generalized Branciari space, this paper develops and reproves some conclusions from the li... more In the generalized Branciari space, this paper develops and reproves some conclusions from the literature.

International Advanced Research Journal in Science, Engineering and Technology, 2024

In this paper, we obtain the necessary and sufficient condition for W^i_{jkh}, N^i_{jkh} and H^i_... more In this paper, we obtain the necessary and sufficient condition for W^i_{jkh}, N^i_{jkh} and H^i_{jkh} to be recurrent and we get a relationship between them. The projection on indicatrix with respect to Cartan connection has been studied.

AIP Conference Proceedings, 2024

In this paper, we discuss the relationship between WijkhW^i _{jkh}Wijkh and PijkhP^i _{jkh}Pijkh in generalized r... more In this paper, we discuss the relationship between WijkhW^i _{jkh}Wijkh and PijkhP^i _{jkh}Pijkh in generalized recurrent and birecurrent Finsler space. Further, we obtain the condition for WijkhW^i _{jkh}Wijkh that is a generalized recurrent and birecurrent tensor. Additionally, several corollaries have been obtained.

Int. Jr. of Contemp. Res. in Multi., 2024

Deviating from the traditional framework to prove the existence and uniqueness of a fixed point a... more Deviating from the traditional framework to prove the existence and uniqueness of a fixed point and replacing the fixed number in the Banach contraction principle with a function that has its conditions is one of the most difficult challenges facing studies concerned with the fixed point, which researchers took on recently. Success in such studies has a wide applied impact in many areas of mathematics, reflecting positively on various applied sciences. In this study, we establish new fixed point theorems for contractive mapping in a complete metric space using some helping functions via Caristitype.

International Journal of Research Publication and Reviews, 2024

A basic version of the Hardy-Rogers fixed point theorem is presented in this study.

Journal of Drug Designing and Bioinformatics, 2023

In this paper, Cauchy-Schwarz inequality on n-inner product spaces is reproved, and notions of or... more In this paper, Cauchy-Schwarz inequality on n-inner product spaces is reproved, and notions of orthogonality on n-normed spaces are introduced. This is the first approach to orthogonality types in such spaces.