Year 2022,
Volume: 6 Issue: 1, 74 - 92, 31.03.2022
Sana Hadj Amor
,
Ameni Remadı
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
Sana Hadj Amor
,
Ameni Remadı
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.