EXISTENCE AND UNIQUENESS OF COMMON FIXED POINT SOLUTION FOR INTEGRAL EQUATION VIA COMPLEX VALUED METRIC SPACE USING CLASS FUNCTION.

SHINDE, SOPAN RAOSAHEB; Pathak, Renu

doi:10.21608/ejmaa.2024.226939.1054

EXISTENCE AND UNIQUENESS OF COMMON FIXED POINT SOLUTION FOR INTEGRAL EQUATION VIA COMPLEX VALUED METRIC SPACE USING CLASS FUNCTION.

Document Type : Regular research papers

Authors

SOPAN RAOSAHEB SHINDE ¹
Renu Pathak ²

¹ sandip university nasik

² Nasik, Maharashtra, India

10.21608/ejmaa.2024.226939.1054

Abstract

The manuscript aims to introduce a unified approach for solving the Urysohn integral equation through common fixed points. It is structured into two main sections. The first section establishes fixed point results by utilizing class functions for pairs of weakly compatible mappings. These mappings satisfy a rational-type contractive condition within the context of CVMS. The second section focuses on deriving a common solution for the integral equation, emphasizing its uniqueness. The study further validates the CFP theorem under a more generalized rational-type contraction criterion, employing both class functions and four self-mappings. Notably, the presented results not only extend but also enhance existing findings in the field. we validate CFP theorem under more generalized rational type contraction condition usuing class function and four self mapping. The manuscript concludes with an application of the integral equation, highlighting its practical relevance. In summary, the manuscript offers a comprehensive framework for Urysohn integral equation solutions and contributes significantly to the existing body of knowledge.

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