Best proximity of proximal $\mathcal{F}^*$-weak contraction

محورهای موضوعی : Fixed point theory

M. Salamatbakhsh ¹ , R. H. Haghi ² , K. Fallahi ³

1 - Department of Mathematics, Payame Noor University, Tehran, Iran
2 - Department of Mathematics, Payame Noor University, Tehran, Iran
3 - Department of Mathematics, Payame Noor University, Tehran, Iran

تاریخ دریافت : 1400/10/24 تاریخ پذیرش : 1400/12/13 تاریخ انتشار : 1400/12/14

کلید واژه: Best Proximity point‎, ‎approximatively compact‎, ‎cyclically Cauchy sequence‎, ‎uniform approximation‎, ‎quasi-continuous, ‎proximal $mathcal{F}^{*}$-weak‎ ‎contraction‎, $mathcal{S}$-approximation‎,

چکیده مقاله :

‎Best proximity point‎ ‎theorems for self-mappings were investigated with different‎ ‎conditions on spaces for contraction mappings‎. ‎In this‎ ‎paper‎, ‎we prove best proximity point theorems for proximal $\mathcal{F}^{*}$-weak contraction mappings‎.

منابع و مأخذ:

[1] A. Aghanians, K. Fallahi, Fixed points for Chatterjea contractions on a metric space with a graph, Int. J. Nonlinear Anal. Appl. 7 (2) (2016), 49-58.

[2] A. Aghanians, K. Fallahi, On quasi-contractions in metric spaces with a Graph, Hacettepe J. Math. Stat. 45 (4) (2016), 1033-1047.

[3] W. M. Alfaqih, M. Imdad, R. Gurban, An observation on F-weak contractions and discontinuity at the fixed point with an application, J. Fixed Point Theory Appl. 22 (2020), 22:66.

[4] M. Berzig, E. Karapinar, S. Radenovi´ c, Z. Kadelburg, D. Jandrli´ c, A. Jandrli´ c, Some results on weakly contractive maps, Bull. Iran. Math. Soc. 38 (3) (2012), 625-645.

[5] R. Espinola, G. Sankara, R. Kosuru, P. Veeramani, Pythagorean property and best proximity point theorems, J. Optim. Theory. Appl. 164 (2015), 534-550.

[6] M. Imdad, Q. Khan, W. M. Alfaqih, R. Gubran, A relation theoretic (F,R)−contraction principle with applications to matrix equations, Bull. Math. Anal. Appl. 10 (1) (2018), 1-12.

[7] R. Kannan, Some results on fixed points, Bull. Calcutta. Math. Soc. 60 (1968), 71-76.

[8] W. Kirk, S. Reich, P. Veeramani, Proximal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim. 24 (2003), 851-862.

[9] W. Kirk, PS. Sinarsan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed point theory. 4 (1) (2003), 79-89.

[10] R. Pant, Discontinuity and fixed points, J. Math. Anal. Appl. 240 (1) (1999), 284-289.

[11] B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Am. Math. Soc. 226 (1977), 257-290.

[12] B. E. Rhoades, Contractive definitions and continuity, Contemp. Math. 72 (1988), 233-245.

[13] S. Sadiq Basha, Best proximity points: Optimal Solutions, J. Optim. Theory. Appl. 151 (2011), 210-216.

[14] S. Sadiq Basha, Best proximity point theorems in the frameworks of fairly and proximally complete spaces, J. Fixed Point Theory Appl. 19 (3) (2017), 1939-1951.

[15] S. Sadiq Basha, Extensions of Banach’s contraction principle, Numer. Funct. Anal. Optim. 31 (5) (2010), 569-579.

[16] S. Sadiq Basha, N. Shahzad, C. Vetro, Best proximity point theorems for proximal cyclic contraction, J. Fixed Point Theory Appl. 19 (4) (2017), 2647-2661.

[17] S. Sadiq Basha, P. Veeramani, Best proximity pair theorems for multifunctions and with open fibres, J. Approx. Theory. 103 (2000), 119-129.

[18] N. A. Secelean, Weak F-contractions and some fixed point results, Bull. Iran. Math. Soc. 42 (3) (2016), 779-798.

[19] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (2012), 94:6.

[20] D. Wardowski, N. Van Dung, Fixed points of F-weak contractions on complete metric spaces, Demonstr. Math. 47 (1) (2014), 146-155.

[21] K. Wlodarczyk, R. Plebaniak, A. Banach, Erratum to: “Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces, Nonlinear Anal. 70 (2009), 3332-3341.