NEW GERAGHTY TYPE CONDENSING OPERATORS AND SOLVABILITY OF NONLINEAR QUADRATIC VOLTERRA-STIELTJES INTEGRAL EQUATION

. The true motivation of this article is to provide sufficient conditions with the aid of Geraghty type condensing operators that guarantee the existence of a solution of nonlinear quadratic Volterra-Stieltjes integral equation. We also address several new fixed point theorems that ensure the existence of a fixed point for Geraghty type condensing operators in real Banach spaces. An example and numerical approximations are presented to justify the basis of our results.

[1]  P. Kumam,et al.  A new Popov's subgradient extragradient method for two classes of equilibrium programming in a real Hilbert space , 2020, Optimization.

[2]  Poom Kumam,et al.  The Inertial Sub-Gradient Extra-Gradient Method for a Class of Pseudo-Monotone Equilibrium Problems , 2020, Symmetry.

[3]  H. Rehman,et al.  Fixed point theorems for Meir-Keeler condensing operators in partially ordered Banach spaces , 2019 .

[4]  G. Rybicki.  Radiative transfer , 2019, Climate Change and Terrestrial Ecosystem Modeling.

[5]  Poom Kumam,et al.  Generalizations of Darbo’s fixed point theorem for new condensing operators with application to a functional integral equation , 2019, Demonstratio Mathematica.

[6]  Alexander G. Ramm,et al.  Integral equations and applications , 2015 .

[7]  Mohammad Mursaleen,et al.  A generalization of Darbo's theorem with application to the solvability of systems of integral equations , 2014, J. Comput. Appl. Math..

[8]  N. Merentes,et al.  Bounded Variation and Around , 2013 .

[9]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[10]  W. Orlicz,et al.  COMPOSING FUNCTIONS OF BOUNDED ^-VARIATION , 2010 .

[11]  Józef Banaś,et al.  Measures of Noncompactness in Banach Spaces , 1980 .

[12]  Michael A. Geraghty,et al.  On contractive mappings , 1973 .

[13]  J. Nieto,et al.  Existence of tripled fixed points and solution of functional integral equations through a measure of noncompactness , 2019 .

[14]  J. Banaś,et al.  Solutions of a quadratic Volterra–Stieltjes integral equation in the class of functions converging at infinity , 2018 .

[15]  N. Merentes,et al.  Measures of Noncompactness in the Space of Continuous and Bounded Functions Defined on the Real Half-Axis , 2017 .

[16]  J. Banaś,et al.  Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness , 2017 .

[17]  J. Banaś,et al.  Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity , 2017 .

[18]  Józef Banas,et al.  An application of a measure of noncompactness in the study of asymptotic stability , 2003, Appl. Math. Lett..

[19]  Gabriele Darbo,et al.  Punti uniti in trasformazioni a codominio non compatto , 1955 .

[20]  Rendiconti del Seminario Matematico della Università di Padova , 2022 .