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Papers by Mohammad I Bhat

Applied Mathematics and Computation, 2012

In this paper, we introduce and study a new system of (A, η)-accretive mapping inclusions in Bana... more In this paper, we introduce and study a new system of (A, η)-accretive mapping inclusions in Banach spaces. Using the resolvent operator associated with (A, η)-accretive mappings, we suggest a new general algorithm and establish the existence and uniqueness of solutions for this system of (A, η)-accretive mapping inclusions. Under certain conditions, we discuss the convergence and stability of iterative sequence generated by the algorithm. Our results extend, improve and unify many known results on variational inequalities and variational inclusions.

I n t hi s pap er, we c on si der a cl a ss of im pl i ci t v ari ati onal i nequal i t i es i n ... more I n t hi s pap er, we c on si der a cl a ss of im pl i ci t v ari ati onal i nequal i t i es i n Banach space s a nd pr ov e i t s equiv al ence wi t h a cl a ss of W i ener-Hopf equat i ons. F urt her, u si ng t hi s equiv al ence, we su gge st an d anal yze a Mann t ype i t erat iv e al gori t hm f or f i ndi ng t he appro pri at e sol ut i on of t he cl a ss of W i ener-Hopf equat i on a nd di scu s s i t s conv ergence cri t eri a. T he t h eorem s i n t he p ape r ex t end an d im prov e m any known re sul t s i n t he l i t erat ure. Keywords : I m pli cit v ari at i onal i nequal i t y, W i ener-Hopf equat i on, Mann t yp e i t erat iv e al gori t hm, sun ny r et ract i on, ηst rongl y acc ret iv e m appi ng.

Computers & Mathematics with Applications, 2004

ABSTRACT We study a generalized implicit complementarity problem (in short, GICP) in uniformly sm... more ABSTRACT We study a generalized implicit complementarity problem (in short, GICP) in uniformly smooth Banach space and show that it is equivalent to a fixed point problem. Using this equivalence we analyze an iterative algorithm for GICP. Further, we prove the existence of solution and discuss the convergence analysis of the developed iterative algorithm. The theorems presented in this paper generalize, improve and unify the corresponding known results for the complementarity problems in Hilbert spaces.

We consider a general quasi-variational inequality problem involving nonlinear, non-convex and no... more We consider a general quasi-variational inequality problem involving nonlinear, non-convex and nondifferentiable term in uniformly smooth Banach space. Using retraction mapping and fixed point method, we study the existence of solution of general quasi-variational inequality problem and discuss the convergence analysis and stability of a three-step iterative algorithm for general quasi-variational inequality problem. The the-orems presented in this paper generalize, improve, and unify many previously known results in the literature. Copyright © 2006 K. R. Kazmi and M. I. Bhat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, dis-tribution, and reproduction in any medium, provided the original work is properly cited. 1.

In this paper, we give the notion of P-g-proximal mapping, an extension of P-proximal mapping giv... more In this paper, we give the notion of P-g-proximal mapping, an extension of P-proximal mapping given by Ding and Xia [J. Comput. Appl. Math. 147 (2002) 369], for a nonconvex lower semicontinuous g-subdifferentiable proper functional on Banach space and prove its existence and Lipschitz continuity. Further, we consider a class of generalized set-valued variational-like inclusions in Banach space and show its equivalence with a class of implicit Wiener-Hopf equations using the concept of P-g-proximal mapping. Using this equivalence, we propose a new class of iterative algorithms for the class of generalized set-valued variational-like inclusions. Furthermore, we prove the existence of solution of generalized set-valued variational-like inclusions and discuss the convergence criteria and the stability of the iterative algorithm.

Journal of the International Academy of Periodontology, Jan 8, 2016

Loss of tooth-supporting structures results in tooth mobility. Increased tooth mobility adversely... more Loss of tooth-supporting structures results in tooth mobility. Increased tooth mobility adversely affects function, aesthetics, and the patient's comfort. Splints are used to over-come all these problems. When faced with the dilemma of how to manage periodontally compromised teeth, splinting of mobile teeth to stronger adjacent teeth is a viable option. This prolongs the life expectancy of loose teeth, gives stability for the periodontium to reattach, and improves comfort, function and aesthetics. Although splinting has been used since ancient times, it has been a topic of controversy because of its ill effects on oral health, including poor oral hygiene and adverse effects on supporting teeth. There have been considerable advancements in the materials used for splinting, resulting in fewer ill effects. This article is intended to provide the clinicians with an updated overview of splinting, types and classification of splints, with their indications, contraindications,rationale...

Applied Mathematics and Computation, 2012

In this paper, we introduce and study a new system of (A, η)-accretive mapping inclusions in Bana... more In this paper, we introduce and study a new system of (A, η)-accretive mapping inclusions in Banach spaces. Using the resolvent operator associated with (A, η)-accretive mappings, we suggest a new general algorithm and establish the existence and uniqueness of solutions for this system of (A, η)-accretive mapping inclusions. Under certain conditions, we discuss the convergence and stability of iterative sequence generated by the algorithm. Our results extend, improve and unify many known results on variational inequalities and variational inclusions.

I n t hi s pap er, we c on si der a cl a ss of im pl i ci t v ari ati onal i nequal i t i es i n ... more I n t hi s pap er, we c on si der a cl a ss of im pl i ci t v ari ati onal i nequal i t i es i n Banach space s a nd pr ov e i t s equiv al ence wi t h a cl a ss of W i ener-Hopf equat i ons. F urt her, u si ng t hi s equiv al ence, we su gge st an d anal yze a Mann t ype i t erat iv e al gori t hm f or f i ndi ng t he appro pri at e sol ut i on of t he cl a ss of W i ener-Hopf equat i on a nd di scu s s i t s conv ergence cri t eri a. T he t h eorem s i n t he p ape r ex t end an d im prov e m any known re sul t s i n t he l i t erat ure. Keywords : I m pli cit v ari at i onal i nequal i t y, W i ener-Hopf equat i on, Mann t yp e i t erat iv e al gori t hm, sun ny r et ract i on, ηst rongl y acc ret iv e m appi ng.

Computers & Mathematics with Applications, 2004

ABSTRACT We study a generalized implicit complementarity problem (in short, GICP) in uniformly sm... more ABSTRACT We study a generalized implicit complementarity problem (in short, GICP) in uniformly smooth Banach space and show that it is equivalent to a fixed point problem. Using this equivalence we analyze an iterative algorithm for GICP. Further, we prove the existence of solution and discuss the convergence analysis of the developed iterative algorithm. The theorems presented in this paper generalize, improve and unify the corresponding known results for the complementarity problems in Hilbert spaces.

We consider a general quasi-variational inequality problem involving nonlinear, non-convex and no... more We consider a general quasi-variational inequality problem involving nonlinear, non-convex and nondifferentiable term in uniformly smooth Banach space. Using retraction mapping and fixed point method, we study the existence of solution of general quasi-variational inequality problem and discuss the convergence analysis and stability of a three-step iterative algorithm for general quasi-variational inequality problem. The the-orems presented in this paper generalize, improve, and unify many previously known results in the literature. Copyright © 2006 K. R. Kazmi and M. I. Bhat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, dis-tribution, and reproduction in any medium, provided the original work is properly cited. 1.

In this paper, we give the notion of P-g-proximal mapping, an extension of P-proximal mapping giv... more In this paper, we give the notion of P-g-proximal mapping, an extension of P-proximal mapping given by Ding and Xia [J. Comput. Appl. Math. 147 (2002) 369], for a nonconvex lower semicontinuous g-subdifferentiable proper functional on Banach space and prove its existence and Lipschitz continuity. Further, we consider a class of generalized set-valued variational-like inclusions in Banach space and show its equivalence with a class of implicit Wiener-Hopf equations using the concept of P-g-proximal mapping. Using this equivalence, we propose a new class of iterative algorithms for the class of generalized set-valued variational-like inclusions. Furthermore, we prove the existence of solution of generalized set-valued variational-like inclusions and discuss the convergence criteria and the stability of the iterative algorithm.

Journal of the International Academy of Periodontology, Jan 8, 2016

Loss of tooth-supporting structures results in tooth mobility. Increased tooth mobility adversely... more Loss of tooth-supporting structures results in tooth mobility. Increased tooth mobility adversely affects function, aesthetics, and the patient's comfort. Splints are used to over-come all these problems. When faced with the dilemma of how to manage periodontally compromised teeth, splinting of mobile teeth to stronger adjacent teeth is a viable option. This prolongs the life expectancy of loose teeth, gives stability for the periodontium to reattach, and improves comfort, function and aesthetics. Although splinting has been used since ancient times, it has been a topic of controversy because of its ill effects on oral health, including poor oral hygiene and adverse effects on supporting teeth. There have been considerable advancements in the materials used for splinting, resulting in fewer ill effects. This article is intended to provide the clinicians with an updated overview of splinting, types and classification of splints, with their indications, contraindications,rationale...