In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the...In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems. As an application, we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables.展开更多
In this paper,we study the existence of solutions to an implicit functional equation involving a fractional integral with respect to a certain function,which generalizes the Riemann-Liouville fractional integral and t...In this paper,we study the existence of solutions to an implicit functional equation involving a fractional integral with respect to a certain function,which generalizes the Riemann-Liouville fractional integral and the Hadaniard fractional integral.We establish an existence result to such kind of equations using a generalized version of Darbo＇s theorem associated to a certain measure of nonconipactness.Some examples are presented.展开更多
We investigate a q-fractional integral equation with supremum and prove an existence theorem for it. We will prove that our q-integral equation has a solution in C [0, 1] which is monotonic on [0, 1]. The monotonicity...We investigate a q-fractional integral equation with supremum and prove an existence theorem for it. We will prove that our q-integral equation has a solution in C [0, 1] which is monotonic on [0, 1]. The monotonicity measures of noncompactness due to Banaśand Olszowy and Darbo’s theorem are the main tools used in the proof of our main result.展开更多
文摘In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems. As an application, we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables.
基金support by the Ministerio de Economica y Competitividad of Spain under grant MTM2013-43014-PXUNTA under grants R2014/002 and GRC2015/004+1 种基金co-financed by the European Community fund FEDERextends his appreciation to Distinguished Scientist Fellowship Program(DSFP)at King Saud University(Saudi Arabia)
文摘In this paper,we study the existence of solutions to an implicit functional equation involving a fractional integral with respect to a certain function,which generalizes the Riemann-Liouville fractional integral and the Hadaniard fractional integral.We establish an existence result to such kind of equations using a generalized version of Darbo＇s theorem associated to a certain measure of nonconipactness.Some examples are presented.
文摘We investigate a q-fractional integral equation with supremum and prove an existence theorem for it. We will prove that our q-integral equation has a solution in C [0, 1] which is monotonic on [0, 1]. The monotonicity measures of noncompactness due to Banaśand Olszowy and Darbo’s theorem are the main tools used in the proof of our main result.
