Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 17 (2022), 367 -- 395

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This work is licensed under a Creative Commons Attribution 4.0 International License.

SOLVABILITY OF INTEGRAL EQUATIONS THROUGH FIXED POINT THEOREMS: A SURVEY

Usha Bag and Reena Jain

Abstract. This paper surveys regarding solutions of linear and nonlinear integral equations through fixed point theorem. Banach's contraction mapping principle is the most widely applied fixed point theorem in all of analysis with special applications to the theory of integral equations. Over a decade researchers have generalized the definition of a metric space and using the technique of fixed point have found solutions to many linear and nonlinear Volterra-Fredholm integral equations.

2020 Mathematics Subject Classification: Primary 47H10, Secondary54H25
Keywords: Fixed point; b-metric spaces; extended b-metric spaces; dislocated extended b-metric space; Rational weak F-contraction; Metric space

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Usha Bag
Mathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University,
466114, Madhya Pradesh, India.
e-mail: usha.bag2019@vitbhopal.ac.in




Reena Jain
Mathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University,
466114, Madhya Pradesh, India.
e-mail: reena.jain@vitbhopal.ac.in

http://www.utgjiu.ro/math/sma