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Year 2022, Volume: 6 Issue: 1, 74 - 92, 31.03.2022
https://doi.org/10.31197/atnaa.983573

Abstract

References

  • [1] A. Aghajani, M. Mursaleen, A. Shole Haghighi, Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness, Acta. Math. Sci. 35B (3) (2015), 552-566.
  • [2] D. Averna, S.A. Marano, Existence of solutions for operator inclusions, a unified approach. Rend. Sem. Mat. Univ. Padova 102, (1999).
  • [3] J. Bana’s and M.-A. Taoudi, Fixed points and solutions of operator equations for the weak topology in Banach algebras, Taiwanese J. Math. 18 (2014), 871-893.
  • [4] M. Belhadj, A. Ben Amar and M. Boumaiza, Some fixed point theorems for Meir-Keeler condensing operators and appli- cation to a system of integral equations, Bull. Belg. Math. Soc. Simon Stevin 26 (2019), 223-239.
  • [5] A. Ben Amar, Krasnoselskii type fixed point theorems for multi-valued mappings with weakly sequentially closed graph, Ann. Univ. Ferrara 58 (2012), 1-10.
  • [6] A. Ben Amar, M. Boumaiza and D. O’Regan, Hybrid fixed point theorems for multivalued mappings in Banach algebras under a weak topology setting, J. Fixed Point Theory Appl. DOI 10.1007/s11784-016-0289-9.
  • [7] A. Ben Amar, S. Chouayekh and A. Jeribi, Fixed point theory in a new class of Banach algebras and application, Afr. Mat. 24 (2013), no. 4, 725-724.
  • [8] A. Ben Amar, S. Chouayekh, A. Jeribi, New fixed point theorems in Banach algebras under weak topology features and applications to nonlinear integral equations, Journal of Functional Analysis 259 (2010), 2215-2237.
  • [9] A. Ben Amar, S. Derbel, D. O’Regan and T. Xiang, Fixed point theory for countably weakly condensing maps and multimaps in non-separable Banach spaces, Journal of Fixed Point Theory and Applications 21.1 (2019), 1-25.
  • [10] A. Ben Amar, A. Jeribi and R. Moalla, Leray-Schauder alternatives in Banach algebras involving three operators with application, Fixed Point Theory 15 (2014), no. 2, 359-372.
  • [11] A. Ben Amar, A. Sikorska-Nowak, On Some Fixed Point Theorems for 1-Set Weakly Contractive Multi-Valued Mappings with Weakly Sequentially Closed Graph, Advances in Pure Mathematics, 2011, 1, 163-169.
  • [12] De Blasi, S. Francesco , On a property of the unit sphere in a Banach space, Bulletin math´ ematique de la Soci´ et´ e des Sciences Math´ ematiques de la R´ epublique Socialiste de Roumanie, 1977, 259–262, JSTOR.
  • [13] G. Bonanno, S.A. Marano, Positive solutions of elliptic equations with discontinuous nonlinearities, Topol. Methods Non- linear Anal. 8, 263-273 (1996).
  • [14] T. Cardinali, F. Papalini, Fixed point theorems for multifunctions in topological vector spaces, J. Math. Anal. Appl. 186 (1994),769-777.
  • [15] T. Cardinali, F. Rubbioni, Multivalued fixed point theorems in terms of weak topology and measure of weak noncompact- ness, J. Math. Anal. Appl. 405, 409-415 (2013).
  • [16] S. Chandrasekhar, Radiative Transfer, Dover Publications Inc.: New York, NY, USA, 1960.
  • [17] B.C. Dhage, Existence results for neutral functional diffrential inclusions in Banach algebras, Nonlinear Analysis 64 (2006) 1290-1306.
  • [18] B. C. Dhage, Multivalued operators and fixed point theorems in Banach algebras, I. Taiwanese J. Math. 10 (2006), 1025- 1045.
  • [19] B.C. Dhage, On some variants of Schauders fixed point principle and applications to nonlinear integral equations, J. Math. Phys. Sci. 25 (1988) 603-611.
  • [20] R. E. Edwards, Functional Analysis, Theory and Appli-cations, Reinhart and Winston, New York, 1965.
  • [21] H. George, J.R. Pimbley, Positive solutions of a quadratic integral equation, Arch. Ration. Mech. Anal. 1967,24, 107-127.
  • [22] M. Ghiocel, A. Petrusel and G. Petrusel, Topics in Nonlinear Analysis and Application to Mathematical Economics, Cluj-Napoca, 2007.
  • [23] G. Gripenberg, On some epidemic models, Q. Appl. Math. 1981, 39, 317-327.
  • [24] J.K. Hale, Theory of Functional Differential Equations, Springer, New York 1977.
  • [25] N. Hussain, M.A. Taoudi, Krasnosel’skii-type fixed point theorems with applications to Volterra integral equations, Fixed Point Theory Appl. 2013, 196(2013).
  • [26] L. Kurz, P. Nowosad, B.R. Saltzberg, On the solution of a quadratic integral equation arising in signal design, J. Franklin Inst. 1966, 281, 437-454.
  • [27] T. C. Lim, On characterizations of Meir-Keeler contractive maps, Nonlinear Anal. 46 (2001), 113-120.
  • [28] K. Musial, Pettis integral, In: Handbook of Measure Theory, Vol. I, II, NorthHolland, Amsterdam, 2002, 531-58.
  • [29] ] S.K. Ntouyas, Initial and boundary value problems for functional differential equations via topological transversality method : A Survey, Bull. Greek Math. Soc. 40 (1998), 3-41.
  • [30] D. O’Regan, Fixed point theorems for weakly sequentially closed maps, Archivum Mathematicum (Brno) Tomus. 36, 61-70 (2000).
  • [31] D. O’Regan, M.A.Taoudi, Fixed point theorems for the sum of two weakly sequentially continuous mappings, Nonlinear Anal. Nonlinear Anal. 73(2), 283-289 (2010).
  • [32] W. Rudin, Functional Analysis, 2nd ed.; McGraw-Hill: New York, NY, USA, 1991.
  • [33] T. Suzuki, Fixed point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces, Nonlinear Anal. 64 (5) (2006), 971-978.

Solutions of Neutral Differential Inclusions

Year 2022, Volume: 6 Issue: 1, 74 - 92, 31.03.2022
https://doi.org/10.31197/atnaa.983573

Abstract

Motivated by the study of neutral differential inclusions, we establish a new fixed point theorem for multivalued countably Meir-Keeler condensing mappings via an arbitrary measure of weak noncompactness which in turn include the fixed point theorems of Krasnoselskii and Dhage as special cases in non separable spaces.

References

  • [1] A. Aghajani, M. Mursaleen, A. Shole Haghighi, Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness, Acta. Math. Sci. 35B (3) (2015), 552-566.
  • [2] D. Averna, S.A. Marano, Existence of solutions for operator inclusions, a unified approach. Rend. Sem. Mat. Univ. Padova 102, (1999).
  • [3] J. Bana’s and M.-A. Taoudi, Fixed points and solutions of operator equations for the weak topology in Banach algebras, Taiwanese J. Math. 18 (2014), 871-893.
  • [4] M. Belhadj, A. Ben Amar and M. Boumaiza, Some fixed point theorems for Meir-Keeler condensing operators and appli- cation to a system of integral equations, Bull. Belg. Math. Soc. Simon Stevin 26 (2019), 223-239.
  • [5] A. Ben Amar, Krasnoselskii type fixed point theorems for multi-valued mappings with weakly sequentially closed graph, Ann. Univ. Ferrara 58 (2012), 1-10.
  • [6] A. Ben Amar, M. Boumaiza and D. O’Regan, Hybrid fixed point theorems for multivalued mappings in Banach algebras under a weak topology setting, J. Fixed Point Theory Appl. DOI 10.1007/s11784-016-0289-9.
  • [7] A. Ben Amar, S. Chouayekh and A. Jeribi, Fixed point theory in a new class of Banach algebras and application, Afr. Mat. 24 (2013), no. 4, 725-724.
  • [8] A. Ben Amar, S. Chouayekh, A. Jeribi, New fixed point theorems in Banach algebras under weak topology features and applications to nonlinear integral equations, Journal of Functional Analysis 259 (2010), 2215-2237.
  • [9] A. Ben Amar, S. Derbel, D. O’Regan and T. Xiang, Fixed point theory for countably weakly condensing maps and multimaps in non-separable Banach spaces, Journal of Fixed Point Theory and Applications 21.1 (2019), 1-25.
  • [10] A. Ben Amar, A. Jeribi and R. Moalla, Leray-Schauder alternatives in Banach algebras involving three operators with application, Fixed Point Theory 15 (2014), no. 2, 359-372.
  • [11] A. Ben Amar, A. Sikorska-Nowak, On Some Fixed Point Theorems for 1-Set Weakly Contractive Multi-Valued Mappings with Weakly Sequentially Closed Graph, Advances in Pure Mathematics, 2011, 1, 163-169.
  • [12] De Blasi, S. Francesco , On a property of the unit sphere in a Banach space, Bulletin math´ ematique de la Soci´ et´ e des Sciences Math´ ematiques de la R´ epublique Socialiste de Roumanie, 1977, 259–262, JSTOR.
  • [13] G. Bonanno, S.A. Marano, Positive solutions of elliptic equations with discontinuous nonlinearities, Topol. Methods Non- linear Anal. 8, 263-273 (1996).
  • [14] T. Cardinali, F. Papalini, Fixed point theorems for multifunctions in topological vector spaces, J. Math. Anal. Appl. 186 (1994),769-777.
  • [15] T. Cardinali, F. Rubbioni, Multivalued fixed point theorems in terms of weak topology and measure of weak noncompact- ness, J. Math. Anal. Appl. 405, 409-415 (2013).
  • [16] S. Chandrasekhar, Radiative Transfer, Dover Publications Inc.: New York, NY, USA, 1960.
  • [17] B.C. Dhage, Existence results for neutral functional diffrential inclusions in Banach algebras, Nonlinear Analysis 64 (2006) 1290-1306.
  • [18] B. C. Dhage, Multivalued operators and fixed point theorems in Banach algebras, I. Taiwanese J. Math. 10 (2006), 1025- 1045.
  • [19] B.C. Dhage, On some variants of Schauders fixed point principle and applications to nonlinear integral equations, J. Math. Phys. Sci. 25 (1988) 603-611.
  • [20] R. E. Edwards, Functional Analysis, Theory and Appli-cations, Reinhart and Winston, New York, 1965.
  • [21] H. George, J.R. Pimbley, Positive solutions of a quadratic integral equation, Arch. Ration. Mech. Anal. 1967,24, 107-127.
  • [22] M. Ghiocel, A. Petrusel and G. Petrusel, Topics in Nonlinear Analysis and Application to Mathematical Economics, Cluj-Napoca, 2007.
  • [23] G. Gripenberg, On some epidemic models, Q. Appl. Math. 1981, 39, 317-327.
  • [24] J.K. Hale, Theory of Functional Differential Equations, Springer, New York 1977.
  • [25] N. Hussain, M.A. Taoudi, Krasnosel’skii-type fixed point theorems with applications to Volterra integral equations, Fixed Point Theory Appl. 2013, 196(2013).
  • [26] L. Kurz, P. Nowosad, B.R. Saltzberg, On the solution of a quadratic integral equation arising in signal design, J. Franklin Inst. 1966, 281, 437-454.
  • [27] T. C. Lim, On characterizations of Meir-Keeler contractive maps, Nonlinear Anal. 46 (2001), 113-120.
  • [28] K. Musial, Pettis integral, In: Handbook of Measure Theory, Vol. I, II, NorthHolland, Amsterdam, 2002, 531-58.
  • [29] ] S.K. Ntouyas, Initial and boundary value problems for functional differential equations via topological transversality method : A Survey, Bull. Greek Math. Soc. 40 (1998), 3-41.
  • [30] D. O’Regan, Fixed point theorems for weakly sequentially closed maps, Archivum Mathematicum (Brno) Tomus. 36, 61-70 (2000).
  • [31] D. O’Regan, M.A.Taoudi, Fixed point theorems for the sum of two weakly sequentially continuous mappings, Nonlinear Anal. Nonlinear Anal. 73(2), 283-289 (2010).
  • [32] W. Rudin, Functional Analysis, 2nd ed.; McGraw-Hill: New York, NY, USA, 1991.
  • [33] T. Suzuki, Fixed point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces, Nonlinear Anal. 64 (5) (2006), 971-978.
There are 33 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sana Hadj Amor 0000-0003-0993-083X

Ameni Remadı This is me

Publication Date March 31, 2022
Published in Issue Year 2022 Volume: 6 Issue: 1

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