Author

# T. Phaneendra

Bio: T. Phaneendra is an academic researcher from VIT University. The author has contributed to research in topics: Fixed point & Metric space. The author has an hindex of 2, co-authored 10 publications receiving 21 citations.

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01 Jan 2013

TL;DR: In this article, the celebrated Banach contraction mapping theorem and a result of Mustafa and Obiedat in a G-metric space using only elementary properties of greatest lower bound were proved.

Abstract: In this paper, we prove the celebrated Banach contraction mapping theorem and a result of Mustafa and Obiedat in a G-metric space using only elementary properties of greatest lower bound. This idea of using greatest lower bound properties in metric space was ini- tiated by Joseph and Kwack in 1999. Also we introduce the notion of G-contractive xed point and demonstrate that the unique xed point will be a G-contractive xed point for the underlying self-map in both the results. Our proof is highly distinct in repeatedly employing the rect- angle inequality of the G-metric rather than using traditional iterative procedure.

9 citations

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TL;DR: In this article, a generalized contraction type mappings relative to a self-map were studied and it was shown that the common fixed point will be a contractive fixed point of the reference map under a certain condition on the contraction constant.

Abstract: In this paper, we prove a common fixed point theorem for a wider class of generalized contraction type mappings relative to a self-map and show that the common fixed point will be a contractive fixed point of the reference map under certain condition on contraction constant. Our result is a generalization of common fixed point theorems of first author, and of Akkouchi.

4 citations

01 Jan 2013

TL;DR: In this paper, Kannan et al. extended this result to a pair of self-maps on a complete 2-metric space and used only elementary properties of greatest lower bound, and repeatedly employing the symmetry and the tetrahedron inequality.

Abstract: Let (M, i²) be a complete metric space and f a self-map on M such that i²(fx, fy) i£ i¢i²(fx, fy) for all x, y i X, where 0 i£ i¢ <1/2. Kannan proved that f has a unique fixed point p and for each x i M the iterates f, f 2 , … will converge to p. In this paper, we extend this result to a pair of self-maps on a complete 2-metric space. Our technique is remarkable to use only elementary properties of greatest lower bound, and repeatedly employing the symmetry and the tetrahedron inequality of the 2-metric instead of routine iteration procedure. This idea was initiated for only metric spaces

2 citations

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TL;DR: In this article, the authors studied the existence of bounded orbits and contractive fixed points for self-maps in G-metric space, without using the iterations of the iterations.

Abstract: Let f be a self-map on a metric space (X, d) and x0 ∈ X. The orbit Of (x0) at x0 is the sequence of f -iterates 〈x0, fx0, ..., f x0, ...〉. A fixed point p of f is a contractive fixed point if every Of (x0) converges to p. The existence of contractive fixed points for self-maps in metric spaces was investigated by Edelstein [1], Leader and Hoyle in [2], and by Reich [11]. The notion of G-contractive fixed point in a generalized metric space was introduced by the first author and Kumara Swamy in [8] in 2013. This paper devotes to the study of bounded orbits and contractive fixed points for certain self-maps in G-metric space, without using the iterations. AMS Subject Classification: 54H25

2 citations

01 Jan 2011

TL;DR: Using the idea of compatibility of self-maps, due to Gerald Jungck, this paper obtained a modest generalization of Badshah and Singh's result, which was used to obtain a modest generalized version of Singh's results.

Abstract: Using the idea of compatibility of self-maps, due to Gerald Jungck, we obtain a modest generalization of Badshah and Singh’s result.

2 citations

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01 Jan 2002

TL;DR: The introduction to real analysis of real analysis by bartle and sherbert and problems in real analysis advanced calculus on the real axis PDF.

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90 citations

01 Jan 2013

TL;DR: In this article, the celebrated Banach contraction mapping theorem and a result of Mustafa and Obiedat in a G-metric space using only elementary properties of greatest lower bound were proved.

Abstract: In this paper, we prove the celebrated Banach contraction mapping theorem and a result of Mustafa and Obiedat in a G-metric space using only elementary properties of greatest lower bound. This idea of using greatest lower bound properties in metric space was ini- tiated by Joseph and Kwack in 1999. Also we introduce the notion of G-contractive xed point and demonstrate that the unique xed point will be a G-contractive xed point for the underlying self-map in both the results. Our proof is highly distinct in repeatedly employing the rect- angle inequality of the G-metric rather than using traditional iterative procedure.

9 citations

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TL;DR: In this paper , the existence of a fixed ellipse (elliptic disc) in an $ \mathcal{S}- $metric space has been shown to be a viable, productive, and powerful technique for finding a fixed point and fixed circle.

Abstract: We introduce an $ \mathcal{M-} $class function in an $ \mathcal{S-} $metric space which is a viable, productive, and powerful technique for finding the existence of a fixed point and fixed circle. Our conclusions unify, improve, extend, and generalize numerous results to a widespread class of discontinuous maps. Next, we introduce notions of a fixed ellipse (elliptic disc) in an $ \mathcal{S}- $metric space to investigate the geometry of the collection of fixed points and prove fixed ellipse (elliptic disc) theorems. In the sequel, we validate these conclusions with illustrative examples. We explore some conditions which eliminate the possibility of the identity map in the existence of an ellipse (elliptic disc). Some remarks, propositions, and examples to exhibit the feasibility of the results are presented. The paper is concluded with a discussion of activation functions that are discontinuous in nature and, consequently, utilized in a neural network for increasing the storage capacity. Towards the end, we solve the satellite web coupling problem and propose two open problems.

9 citations