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Papers by Dhananjay Gopal

Research paper thumbnail of On fixed point theorems involving altering distances in Menger probabilistic metric spaces

Journal of Inequalities and Applications, 2013

ABSTRACT In this paper, we show by means of an example that the results of Babačev (Appl. Anal. D... more ABSTRACT In this paper, we show by means of an example that the results of Babačev (Appl. Anal. Discrete Math. 6:257-264, 2012) do not hold for the class of t-norms T≤Tp. Further, we prove a fixed point theorem for quasi-type contraction involving altering distance functions which is weaker than that proposed by Babačev but for any continuous t-norm in a complete Menger space. MSC: 47H10, 54H25.

Research paper thumbnail of An altering distance function in fuzzy metric fixed point theorems

Fixed Point Theory and Applications, 2015

Research paper thumbnail of Fixed Point Theorems via Absorbing Maps

The purpose of this paper is to obtain common flxed point theorems by using a new notion of absor... more The purpose of this paper is to obtain common flxed point theorems by using a new notion of absorbing maps in fuzzy metric space. In this paper we illustrate the properties of absorbing maps. Moreover we demonstrate the necessity of absorbing maps to flnd a common flxed point in fuzzy metric spaces and menger spaces. Our result generalizes many known

Research paper thumbnail of Some coincidence and periodic points results in a metric space endowed with a graph and applications

Banach Journal of Mathematical Analysis, 2015

Research paper thumbnail of Fixed Point Theory for Cyclic Weak <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϕ</mi><mo>−</mo></mrow><annotation encoding="application/x-tex">\phi-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">ϕ</span><span class="mord">−</span></span></span></span>contraction in Fuzzy Metric Spaces

Journal of Nonlinear Analysis and Application, 2012

Research paper thumbnail of A Note on Fixed Point Theorems in Menger Space

In the present paper we employ the notion of reciprocal continuity to obtain a common fixed point... more In the present paper we employ the notion of reciprocal continuity to obtain a common fixed point theorem in Menger space in which the fixed point may be a point of discontinuity. We also investigate the relationship between continuity of mappings and reciprocal continuity in the setting of Menger spaces. Our result improves the recent result of Singh and Jain 1 in Menger spaces and extends many known results in metric spaces.

Research paper thumbnail of (φ, ψ)-weak contractions in intuitionistic fuzzy metric spaces

Research paper thumbnail of An alternative approach to “fixed point theorems for occasionally weakly compatible mappings”

The aim of this short communication is to provide an alternative of Bisht and Pant result (2013) ... more The aim of this short communication is to provide an alternative of Bisht and Pant result (2013) [1, Theorem 1.2] in the context of framing proper setting for the application of occasionally weakly compatible mappings.

Research paper thumbnail of Impact of (EA) Property on Common Fixed Point Theorems in Fuzzy Metric Spaces

The purpose of the "Journal of Applied Functional Analysis"(JAFA) is to publish high quality orig... more The purpose of the "Journal of Applied Functional Analysis"(JAFA) is to publish high quality original research articles, survey articles and book reviews from all subareas of Applied Functional Analysis in the broadest form plus from its applications and its connections to other topics of Mathematical Sciences. A sample list of connected mathematical areas with this publication includes but

Research paper thumbnail of Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation

Research paper thumbnail of A note on recently introduced commutative conditions

Research paper thumbnail of Some new fixed point theorems on fuzzy metric spaces

Journal of Intelligent and Fuzzy Systems, 2015

ABSTRACT The aim of this paper is to introduce a new class of contractive mappings such as fuzzy ... more ABSTRACT The aim of this paper is to introduce a new class of contractive mappings such as fuzzy alpha-psi-contractive mappings and to present some fixed point theorems for such mappings in complete fuzzy metric space in the sense of Kramosil and Michalek. The results presented in this paper substantially generalize and extend several comparable results in the existing literature. Also, some examples are given to support the usability of our results.

Research paper thumbnail of Common fixed point results for generalized cyclic contraction mappings

Afrika Matematika, 2013

ABSTRACT

Research paper thumbnail of On fixed point theorems involving altering distances in Menger probabilistic metric spaces

Journal of Inequalities and Applications, 2013

Research paper thumbnail of Some Nonunique Common Fixed Point Theorems in Symmetric Spaces through Property

International Journal of Mathematics and Mathematical Sciences, 2013

We introduce a new class of mappings satisfying the "common limit range property" in symmetric sp... more We introduce a new class of mappings satisfying the "common limit range property" in symmetric spaces and utilize the same to establish common fixed point theorems for such mappings in symmetric spaces. Our results generalize and improve some recent results contained in the literature of metric fixed point theory. Some illustrative examples to highlight the realized improvements are also furnished.

Research paper thumbnail of Common fixed point theorems in modified intuitionistic fuzzy metric spaces with common property (E.A.)

Fixed Point Theory and Applications, 2012

In this paper, we give some new fixed point theorems for contractive type mappings in intuitionis... more In this paper, we give some new fixed point theorems for contractive type mappings in intuitionistic fuzzy metric spaces. We improve and generalize the well-known fixed point theorems of Banach and Edelstein [8] in intuitionistic fuzzy metric spaces. Our main results are intuitionistic fuzzy version of Fang's results . Further, we obtain some applications to validate our main results to product spaces.

Research paper thumbnail of Common fixed points of generalized Meir-Keeler α-contractions

Fixed Point Theory and Applications, 2013

ABSTRACT Motivated by Abdeljawad (Fixed Point Theory Appl. 2013:19, 2013), we establish some comm... more ABSTRACT Motivated by Abdeljawad (Fixed Point Theory Appl. 2013:19, 2013), we establish some common fixed point theorems for three and four self-mappings satisfying generalized Meir-Keeler α-contraction in metric spaces. As a consequence, the results of Rao and Rao (Indian J. Pure Appl. Math. 16(1):1249-1262, 1985), Jungck (Int. J. Math. Math. Sci. 9(4):771-779, 1986), and Abdeljawad itself are generalized, extended and improved. Sufficient examples are given to support our main results.

Research paper thumbnail of Impact of Common Property (E.A.) on Fixed Point Theorems in Fuzzy Metric Spaces

Fixed Point Theory and Applications, 2011

... With a view to generalize some fixed point theorems contained in Imdad and Ali 11, 23 we prov... more ... With a view to generalize some fixed point theorems contained in Imdad and Ali 11, 23 we prove the following fixed point theorem which in turn generalizes several previously known results due to Chugh and Kumar 24 , Turkoglu et al. 25 , Vasuki 18 , and some others. ...

Research paper thumbnail of Some existence and uniqueness theorems on ordered metric spaces via generalized distances

Fixed Point Theory and Applications, 2013

The purpose of this paper is to prove some fixed point theorems in a complete metric space equipp... more The purpose of this paper is to prove some fixed point theorems in a complete metric space equipped with a partial ordering using w-distances together with the aid of altering functions. MSC: 54H25; 47H10

Research paper thumbnail of Metrical common fixed point theorems without completeness and closedness

Fixed Point Theory and Applications, 2012

... MI: mhimdad@yahoo.co.in MA: mujahid@lums.edu.pk ... implicit relation utilized in Ali and Imd... more ... MI: mhimdad@yahoo.co.in MA: mujahid@lums.edu.pk ... implicit relation utilized in Ali and Imdad [3] while the notions of weak compatibility and ... Thus u is a common fixed point of A,B,S and T. Finally, suppose that there exists another common fixed point z of A,B,S and T such that ...

Research paper thumbnail of On fixed point theorems involving altering distances in Menger probabilistic metric spaces

Journal of Inequalities and Applications, 2013

ABSTRACT In this paper, we show by means of an example that the results of Babačev (Appl. Anal. D... more ABSTRACT In this paper, we show by means of an example that the results of Babačev (Appl. Anal. Discrete Math. 6:257-264, 2012) do not hold for the class of t-norms T≤Tp. Further, we prove a fixed point theorem for quasi-type contraction involving altering distance functions which is weaker than that proposed by Babačev but for any continuous t-norm in a complete Menger space. MSC: 47H10, 54H25.

Research paper thumbnail of An altering distance function in fuzzy metric fixed point theorems

Fixed Point Theory and Applications, 2015

Research paper thumbnail of Fixed Point Theorems via Absorbing Maps

The purpose of this paper is to obtain common flxed point theorems by using a new notion of absor... more The purpose of this paper is to obtain common flxed point theorems by using a new notion of absorbing maps in fuzzy metric space. In this paper we illustrate the properties of absorbing maps. Moreover we demonstrate the necessity of absorbing maps to flnd a common flxed point in fuzzy metric spaces and menger spaces. Our result generalizes many known

Research paper thumbnail of Some coincidence and periodic points results in a metric space endowed with a graph and applications

Banach Journal of Mathematical Analysis, 2015

Research paper thumbnail of Fixed Point Theory for Cyclic Weak <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϕ</mi><mo>−</mo></mrow><annotation encoding="application/x-tex">\phi-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">ϕ</span><span class="mord">−</span></span></span></span>contraction in Fuzzy Metric Spaces

Journal of Nonlinear Analysis and Application, 2012

Research paper thumbnail of A Note on Fixed Point Theorems in Menger Space

In the present paper we employ the notion of reciprocal continuity to obtain a common fixed point... more In the present paper we employ the notion of reciprocal continuity to obtain a common fixed point theorem in Menger space in which the fixed point may be a point of discontinuity. We also investigate the relationship between continuity of mappings and reciprocal continuity in the setting of Menger spaces. Our result improves the recent result of Singh and Jain 1 in Menger spaces and extends many known results in metric spaces.

Research paper thumbnail of (φ, ψ)-weak contractions in intuitionistic fuzzy metric spaces

Research paper thumbnail of An alternative approach to “fixed point theorems for occasionally weakly compatible mappings”

The aim of this short communication is to provide an alternative of Bisht and Pant result (2013) ... more The aim of this short communication is to provide an alternative of Bisht and Pant result (2013) [1, Theorem 1.2] in the context of framing proper setting for the application of occasionally weakly compatible mappings.

Research paper thumbnail of Impact of (EA) Property on Common Fixed Point Theorems in Fuzzy Metric Spaces

The purpose of the "Journal of Applied Functional Analysis"(JAFA) is to publish high quality orig... more The purpose of the "Journal of Applied Functional Analysis"(JAFA) is to publish high quality original research articles, survey articles and book reviews from all subareas of Applied Functional Analysis in the broadest form plus from its applications and its connections to other topics of Mathematical Sciences. A sample list of connected mathematical areas with this publication includes but

Research paper thumbnail of Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation

Research paper thumbnail of A note on recently introduced commutative conditions

Research paper thumbnail of Some new fixed point theorems on fuzzy metric spaces

Journal of Intelligent and Fuzzy Systems, 2015

ABSTRACT The aim of this paper is to introduce a new class of contractive mappings such as fuzzy ... more ABSTRACT The aim of this paper is to introduce a new class of contractive mappings such as fuzzy alpha-psi-contractive mappings and to present some fixed point theorems for such mappings in complete fuzzy metric space in the sense of Kramosil and Michalek. The results presented in this paper substantially generalize and extend several comparable results in the existing literature. Also, some examples are given to support the usability of our results.

Research paper thumbnail of Common fixed point results for generalized cyclic contraction mappings

Afrika Matematika, 2013

ABSTRACT

Research paper thumbnail of On fixed point theorems involving altering distances in Menger probabilistic metric spaces

Journal of Inequalities and Applications, 2013

Research paper thumbnail of Some Nonunique Common Fixed Point Theorems in Symmetric Spaces through Property

International Journal of Mathematics and Mathematical Sciences, 2013

We introduce a new class of mappings satisfying the "common limit range property" in symmetric sp... more We introduce a new class of mappings satisfying the "common limit range property" in symmetric spaces and utilize the same to establish common fixed point theorems for such mappings in symmetric spaces. Our results generalize and improve some recent results contained in the literature of metric fixed point theory. Some illustrative examples to highlight the realized improvements are also furnished.

Research paper thumbnail of Common fixed point theorems in modified intuitionistic fuzzy metric spaces with common property (E.A.)

Fixed Point Theory and Applications, 2012

In this paper, we give some new fixed point theorems for contractive type mappings in intuitionis... more In this paper, we give some new fixed point theorems for contractive type mappings in intuitionistic fuzzy metric spaces. We improve and generalize the well-known fixed point theorems of Banach and Edelstein [8] in intuitionistic fuzzy metric spaces. Our main results are intuitionistic fuzzy version of Fang's results . Further, we obtain some applications to validate our main results to product spaces.

Research paper thumbnail of Common fixed points of generalized Meir-Keeler α-contractions

Fixed Point Theory and Applications, 2013

ABSTRACT Motivated by Abdeljawad (Fixed Point Theory Appl. 2013:19, 2013), we establish some comm... more ABSTRACT Motivated by Abdeljawad (Fixed Point Theory Appl. 2013:19, 2013), we establish some common fixed point theorems for three and four self-mappings satisfying generalized Meir-Keeler α-contraction in metric spaces. As a consequence, the results of Rao and Rao (Indian J. Pure Appl. Math. 16(1):1249-1262, 1985), Jungck (Int. J. Math. Math. Sci. 9(4):771-779, 1986), and Abdeljawad itself are generalized, extended and improved. Sufficient examples are given to support our main results.

Research paper thumbnail of Impact of Common Property (E.A.) on Fixed Point Theorems in Fuzzy Metric Spaces

Fixed Point Theory and Applications, 2011

... With a view to generalize some fixed point theorems contained in Imdad and Ali 11, 23 we prov... more ... With a view to generalize some fixed point theorems contained in Imdad and Ali 11, 23 we prove the following fixed point theorem which in turn generalizes several previously known results due to Chugh and Kumar 24 , Turkoglu et al. 25 , Vasuki 18 , and some others. ...

Research paper thumbnail of Some existence and uniqueness theorems on ordered metric spaces via generalized distances

Fixed Point Theory and Applications, 2013

The purpose of this paper is to prove some fixed point theorems in a complete metric space equipp... more The purpose of this paper is to prove some fixed point theorems in a complete metric space equipped with a partial ordering using w-distances together with the aid of altering functions. MSC: 54H25; 47H10

Research paper thumbnail of Metrical common fixed point theorems without completeness and closedness

Fixed Point Theory and Applications, 2012

... MI: mhimdad@yahoo.co.in MA: mujahid@lums.edu.pk ... implicit relation utilized in Ali and Imd... more ... MI: mhimdad@yahoo.co.in MA: mujahid@lums.edu.pk ... implicit relation utilized in Ali and Imdad [3] while the notions of weak compatibility and ... Thus u is a common fixed point of A,B,S and T. Finally, suppose that there exists another common fixed point z of A,B,S and T such that ...