Author
Satish Shukla
Bio: Satish Shukla is an academic researcher from Shri Vaishnav Institute of Technology and Science. The author has contributed to research in topics: Metric space & Fixed point. The author has an hindex of 18, co-authored 73 publications receiving 991 citations.
Papers
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TL;DR: In this article, the authors introduced the simulation function and the notion of Z-contraction with respect to which generalize the Banach contraction principle and unify several known types of contractions involving the combination of d(Tx; Ty) and d(x; y): the related fixed point theorems are also proved.
Abstract: Let (X; d) be a metric space and T : X! X be a mapping. In this work, we introduce the mapping : (0;1) (0;1)! R, called the simulation function and the notion ofZ-contraction with respect to which generalize the Banach contraction principle and unify several known types of contractions involving the combination of d(Tx; Ty) and d(x; y): The related fixed point theorems are also proved.
202 citations
TL;DR: In this paper, the concept of partial b-metric spaces is introduced as a generalization of partial metric and b-measure spaces, and an analog to Banach contraction principle, as well as a Kannan type fixed point result is proved in such spaces.
Abstract: The purpose of this paper is to introduce the concept of partial b-metric spaces as a generalization of partial metric and b-metric spaces. An analog to Banach contraction principle, as well as a Kannan type fixed point result is proved in such spaces. Some examples are given which illustrate the results.
148 citations
112 citations
01 Jan 2015
TL;DR: The concept of rectangular b-metric space was introduced in this article as a generalization of metric space, rectangular metric space (RMS) and b-means space (BMS).
Abstract: The concept of rectangular b-metric space is introduced as a generalization of metric space, rectangular
metric space and b-metric space. An analogue of Banach contraction principle and Kannan's xed point
theorem is proved in this space. Our result generalizes many known results in xed point theory.
75 citations
TL;DR: In this article, some common fixed point theorems for -contractions in 0-complete partial metric spaces were proved and extended, generalize, and unify several known results in the literature.
Abstract: We prove some common fixed point theorems for -contractions in 0-complete partial metric spaces. Our results extend, generalize, and unify several known results in the literature. Some examples are included which show that the generalization is proper.
37 citations
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TL;DR: This paper slightly modify Khojasteh et?al.'s notion of simulation function and investigates the existence and uniqueness of coincidence points of two nonlinear operators using this kind of control functions.
140 citations
TL;DR: In this article, the authors introduce a new concept of generalized metric spaces for which they extend some well-known fixed point results including Banach contraction principle, Ciric fixed point theorem, Ran and Reurings, and a fixed point result due to Nieto and Rodriguez-Lopez.
Abstract: We introduce a new concept of generalized metric spaces for which we extend some well-known fixed point results including Banach contraction principle, Ciric’s fixed point theorem, a fixed point result due to Ran and Reurings, and a fixed point result due to Nieto and Rodriguez-Lopez. This new concept of generalized metric spaces recover various topological spaces including standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces.
109 citations
TL;DR: In this article, the authors generalize a series of fixed point results in the framework of b-metric spaces and exemplify it by extending Nadler's contraction principle for set-valued functions.
Abstract: In this paper, we indicate a way to generalize a series of fixed point results in the framework of b-metric spaces and we exemplify it by extending Nadler’s contraction principle for set-valued functions (see Nadler, Pac J Math 30:475–488, 1969) and a fixed point theorem for set-valued quasi-contraction functions due to Aydi et al. (see Fixed Point Theory Appl 2012:88, 2012).
85 citations