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Fixed points of multivalued convex contractions with application
Abdul Rahim Khan1, Hamed H Al-Sulami2, Muhammad Rashid1
1Department of Mathematics and Statistics, University of Southern Punjab, Multan, Pakistan.
Abstract:
In this work, we establish fixed point outcomes for single- valued convex contraction type mappings in the context of a b-metric space. Some of the new results are extended for a multivalued convex contraction and an F-convex contraction. Thereby, an analogue of the famous Nadler's fixed point theorem for a multivalued convex contraction mapping is obtained. The relation among various contractions is presented in a diagram for an insight in this area of investigations. We apply a special case of Theorem 2.11, to solve a nonlinear Fredholm integral equation for a Chatterjea convex contraction.
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