본문 바로가기
KERD
논문KCI 등재

SOME FIXED POINT THEOREMS IN GENERALIZED DARBO FIXED POINT THEOREM AND THE EXISTENCE OF SOLUTIONS FOR SYSTEM OF INTEGRAL EQUATIONS

Reza Arab
대한수학회 (The Korean Mathematical Society)|2015.01|대한수학회지 (Journal of the KMS)|제52권 제1호|pp. 125-139

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

fixed pointcoupled fixed pointmeasure of noncompactnesssystem of integral equations
주제분류수학

초록

In this paper we introduce the notion of the generalized Darbo fixed point theorem and prove some fixed and coupled fixed point theorems in Banach space via the measure of non-compactness, which generalize the result of Aghajani et al. [6]. Our results generalize, extend, and unify several well-known comparable results in the literature. One of the applications of our main result is to prove the existence of solutions for the system of integral equations.

Abstract

In this paper we introduce the notion of the generalized Darbo fixed point theorem and prove some fixed and coupled fixed point theorems in Banach space via the measure of non-compactness, which generalize the result of Aghajani et al. [6]. Our results generalize, extend, and unify several well-known comparable results in the literature. One of the applications of our main result is to prove the existence of solutions for the system of integral equations.

참고문헌 (17)

  1. R. P. Agarwal, "On the application of measure of noncom-pactness to the existence of solutions for fractional differential equations", Results Math, 55(3-4), pp.221~230 (2009)
  2. A. Aghajani, "Existence of solution for a class of nonlinear Voltrra sigular integral equations", Comput. Math. Appl, 62(3), pp.1215~1227 (2011)
  3. R. P. Agarwal, "Singular Volterra integral equations", Appl. Math. Lett, 13(1), pp.115~120 (2000)
  4. R. P. Agarwal, "Fixed Point Theory and Applications" (2004), Cambridge University Press
  5. A. Aghajani, "A generalization of Darbo’s theorem with application to the solvability of systems of integral equations", J. Comput. Appl. Math, 260, pp.68~77 (2014)
  6. A. Aghajani, "Some generalizations of Darbo fixed point theo-rem and applications", Bull. Belg. Math. Soc. Simon Stevin, 20(2), pp.345~358 (2013)
  7. A. Aghajani, "A coupled fixed point theorem for condensing operators with application to system of integral equations", Journal of Nonlinear and Convex Analysis
  8. I. Altun, "A fixed point theorem for mappings satisfying a general contractive condition of operator type", J. Comput. Anal. Appl, 9(1), pp.9~14 (2007)
  9. J. Banas, "Measures of noncompactness in the space of continuous tempered functions", Demonstratio Math, 14(1), pp.127~133 (1981)
  10. J. Banas, "Measures of Noncompactness in Banach Spaces", Lecture Notes in Pure and Applied Mathematics, 60 (1980)
  11. S. S. Chang, "Coupled Fixed Point Theorems with Applications", J. Korean Math. Soc, 33(3), pp.575~585 (1996)
  12. M. Geraghty, "On contractive mappings", Proc. Amer. Math. Soc, 40, pp.604~608 (1973)
  13. X. Hu, "The global attractivity and asymptotic stability of solution of a nonlinear integral equation", J. Math. Anal. Appl, 321(1), pp.147~156 (2006)
  14. Z. Liu, "Existence and asymptotic stability of solutions to functional-integral equation", Taiwanese J. Math, 11(1), pp.187~196 (2007)
  15. L. Liu, "Existence theorems of global solutions for nonlinear Volterra type integral equations in Banach spaces", J. Math. Anal. Appl, 309(2), pp.638~649 (2005)
  16. M. Mursaleen, "Infinite system of differential equations in some spaces", Abstr. Appl. Anal (2012)[DOI]
  17. M. Mursaleen, "Applications of measures of noncompactness to the infinite system of differential equations in l p spaces", Nonlinear Anal, 75(4), pp.2111~2115 (2012)

관련 논문AI추천

Solvability of some non-linear functional integral equations via measure of noncompactnessDeepak Dhiman, Lakshmi Narayan Mishra, Vishnu Narayan Mishra장전수학회 · Advanced Studies in Contemporary Mathematics2022 · 제32권 제2호AN APPLICATION OF DARBO'S FIXED POINT THEOREM TO A NONLINEAR QUADRATIC INTEGRAL EQUATION OF VOLTERRA TYPE강신민, 엄정석, Zeqing Liu한국수학교육학회 · 이론수학과 교직수학2010 · 제17권 제2호Some results on fixed points for a class of generalized Reich type enriched $F$-contractions with some of its application대한수학회 · 대한수학회논문집2026 · 제41권 제1호Some fixed point theorems for weakly Picard operators in complete metric spaces and applicationsBui The Hung, Doan Trong Hieu대한수학회 · 대한수학회논문집2022 · 제37권 제1호Solvability of some nonlinear integro-differential equations of fractional order via measure of noncompactnesKazem Nouri, Leila Torkzadeh, Somayyeh Dadsetadi한국수학교육학회 · 이론수학과 교직수학2020 · 제27권 제1호EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED NONLINEAR CONTRACTION WITH APPLICATIONSAmrish Handa, Bhavana Deshpande, Shamim Ahmad Thoker영남수학회 · East Asian Mathematical Journal2016 · 제32권 제3호

이 간행물의 다른 논문 (12건)

ON v-MAROT MORI RINGS AND C-RINGSSebastian Ramacher, Alfred Geroldinger, Andreas Reinhartpp. 1-21EXPANDING THE CONVERGENCE DOMAIN FOR CHUN-STANICA-NETA FAMILY OF THIRD ORDER METHODS IN BANACH SPACESAngel Alberto Magrenan, Ioannis Konstantinos Argyros, Santhosh Georgepp. 23-41BROYDEN’S METHOD FOR OPERATORS WITH REGULARLY CONTINUOUS DIVIDED DIFFERENCESAnatoly M. Galperinpp. 43-65REGULAR INJECTIVITY AND EXPONENTIABILITY IN THE SLICE CATEGORIES OF ACTIONS OF POMONOIDS ON POSETSFarideh Farsad, Ali Madanshekafpp. 67-80FINITE GROUPS WHOSE INTERSECTION GRAPHS ARE PLANARSelcuk Kayacan, Ergun Yaraneripp. 81-96
원문 보기