Common best proximity points for proximally F–dominated mappings

• Autorzy: Batra, Rakesh
• Języki publikacji: EN

Abstrakty

EN

The principal aim of this work is to formulate an extension and improvement of the common best proximity point theorem for a pair of non-self mappings, one of which is dominated by the other as proved by Basha. The proposed extension discusses a common best proximity point theorem for a pair of non-self mappings, one of which is F-dominated by the other proximally, for a function F as defined by Wardowski.

Słowa kluczowe

EN

global optimal approximate solution; common best proximity point; common fixed point; proximally F-dominated mappings

• Czasopismo: Fasciculi Mathematici
• Rocznik: 2020
• Tom: nr 63
• Strony: 23--37
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Batra, Rakesh

• Department of Mathematics, Hans Raj College, University of Delhi, Delhi-110007, India,

Bibliografia

• [1] Al-Thagafi M.A., Shahzad N., Best proximity sets and equilibrium pairs for a finite family of multimaps, Fixed Point Theory Appl., (2008) : 457069, 10 pp.
• [2] Al-Thagafi M.A., Shahzad N., Convergence and existence results for best proximity points, Nonlinear Anal., 70(10)(2009), 3665-3671.
• [3] Anuradha J., Veeramani P., Proximal pointwise contraction, Topology Appl., 156(18)(2009), 2942-2948.
• [4] Banach S., Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrale, Fund Math., 3(1922), 133-181.
• [5] Eldred A.A., Kirk W.A., Veeramani P., Proximinal normal structure and relatively nonexpansive mappings, Studia Math., 171(3)(2005), 283-293.
• [6] Fan K., Extensions of two fixed point theorems of F.E. Browder, Math. Z., 112(1969), 234-240.
• [7] Jungck G., Commuting mappings and fixed points, Amer. Math. Monthly, 83(1976), 261-263.
• [8] Reich S., Approximate selections, best approximations, fixed points and invariant sets, J. Math. Anal. Appl., 62(1978), 104-113.
• [9] Sadiq Basha S., Best proximity points: global optimal approximate solution, J. Global Optim., (2010), DOI:10.1007/s10898-009-9521-0.
• [10] Sadiq Basha S., Extensions of Banach’s contraction principle, Numer. Funct. Anal. Optim., 31(2010), 569-576.
• [11] Sankar Raj V., Veeramani P., Best proximity pair theorems for relatively nonexpansive mappings, Appl. Gen. Topol., 10(1)(2009), 21-28.
• [12] Wlodarczyk K., Plebaniak R., Banach A., Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces, Nonlinear Anal., 70(9)(2009), 3332-3341.
• [13] Abkar A., Gabeleh M., Global optimal solutions of noncyclic mappings in metric spaces, J. Optim. Theory Appl., 153(2012), 298-305.
• [14] Abkar A., Gabeleh M., A best proximity point theorem for Suzuki type contraction non-self-mappings, Fixed Point Theory, 14(2013), 281-288.
• [15] Sadiq Basha S., Discrete optimization in partially ordered sets, J. Glob. Optim., 54(2012), 511-517.
• [16] Raj V.S., A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear Anal., 74(2011), 4804-4808.
• [17] Choudhury B.S., Maity P., Konar P., A global optimality result using non-self-mappings, Opsearch, 51(2014), 312-320.
• [18] Choudhury B.S., Maity P., Metiya N., Best proximity point theorems with cyclic mappings in setvalued analysis, Indian J. Math., 57(2015), 79-102.
• [19] Dimri R.C., Semwal P., Best proximity results for multivalued mappings, Int. J. Math. Anal., 7(2013), 1355-1362.
• [20] Gabeleh M., Proximal weakly contractive and proximal nonexpansive non-self-mappings in metric and Banach spaces, J. Optim. Theory Appl., 158(2013), 615-625.
• [21] Gabeleh M., Best proximity point theorems via proximal non-self mappings, J. Optim. Theory Appl., 164(2015), 565-576.
• [22] Gupta A., Rajput S.S., Kaurav P.S., Coupled best proximity point theorem in metric spaces, Int. J. Anal. Appl., 4(2014), 201-215.
• [23] Hussain N., Kutbi M.A., Salimi P., Best proximity point results for modified α-ψ-proximal rational contractions, Abstr. Appl. Anal., 2013(2013), Article ID 927457.
• [24] Karapinar E., Erhan I.M., Best proximity point on different type contractions, Appl. Math. Inf. Sci., 5(3)(2011), 558-569.
• [25] Sadiq Basha S., Common best proximity points: global minimal solutions, Top, 21(1)(2013), 182-188, DOI 10.1007/s11750-011-0171-2.
• [26] Sadiq Basha S., Veeramani P., Best proximity pair theorems for multi-functions with open fibres, J. Approx. Theory, 103(2000), 119-129.
• [27] Wardowski D., Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 94(2012).

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).

Identyfikatory

DOI

10.21008/j.0044-4413.2020.0002