New classes of control functions for nonlinear contractions and applications

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:7 Issue:1
New classes of control functions for nonlinear contractions and applications

New classes of control functions for nonlinear contractions and applications

Pages : 29-40

View : 779 | Download : 301

Publication Date : 2023-03-31

Article Type : Research Paper

Abstract :We initiate the use of sub and super homogeneous control functions for nonlinear contractions in complete metric spaces and establish new fixed point theorems. Moreover, we develop other variants of control functions for the fixed point theorems of Boyd-Wong [2] and Matkowski [3]. As application, we present new sufficient conditions ensuring the existence of solutions to some classes of integral equations of Fredholm and Volterra type.
Keywords : Fixed Point Theorems, Contraction type mappings, Fredholm and Volterra integral equations

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