Analytical Solution for a Periodic Boundary Random-Value Problem via Stochastic Fixed Points with PPF Dependence Technique
Abstract
In this paper, some random common fixed point and coincidence point theorems are established with PPF dependence for generalized random contractions in a separable Banach space. Our results introduce stochastic versions and extensions of recent results as [3, 21, 25] and others. In addition, an application to establish PPF dependent solution of a periodic boundary random-valued problem is given to illustrate the usability of obtained results. valued problem is given to illustrate usability of the obtained results.References
R. P. Agarwal, N. Hussain, and M. A. Taoudi, Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations, Abstr. Appl. Anal., Art. ID 245872, pp. 1–15, 2012.
R. P. Agarwal, P. Kumam, and W. Sintunavarat, PPF dependent fixed point theorems for an αc-admissible non-self mapping in the Razumikhin class, Fixed Point Theory and Appl., vol. 280, pp. 1-14, 2013.
S. R. Bernfeld, V. Lakshmikantham, and Y. M. Reddy, Fixed point theorems of operators with PPF dependence in Banach spaces, Applicable Anal., Vol. 6, pp. 271–280, 1977.
A. T. Bharucha-Reid, Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc., vol. 82, No. 5, pp. 641–657, 1976.
B. C. Dhage, Fixed point theorems with PPF dependence and functional differential equations, Fixed Point Theory, vol. 13, no. 2,pp. 439–452, 2012.
B. C. Dhage, On some common fixed point theorems with PPF dependence in Banach spaces, J. Nonlinear Sci. Appl., vol. 5, no. 3,pp. 220–232, 2012.
B. C. Dhage, Some basic random fixed point theorems with PPF dependence and functional random differential equations, Differ. Equ. Appl., vol. 4 no. 2, PP. 181–195, 2012.
Z. Drici, F.A. Mcrae, and J. Vasundhara Devic, Fixed-point theorems in partially ordered metric spaces for operators with PPF dependence, Nonlinear Analysis, vol. 67, pp. 641-647, 2017.
Z. Drici, F. A. Mcrae, and J. V. Devi, Fixed point theorems for mixed monotone operators with PPF dependence, Nonlinear Anal.,vol. 69, no. 2, pp. 632–636, 2008.
D. Duki´ c, Z. Kadelburg, and S. Radenovi´ c, Fixed Points of Geraghty-Type Mappings in arious Generalized Metric Spaces, Abstr. Appl. Anal., vol. 2011, pp. 1-13, 2011.
M. Geraghty, On contractive mappings, Proc. Amer. Math. Soc.,vol. 40, pp. 604–608, 1973.
P. Hans, Random fixed point theorems, Transactions of the first Prague conference on information theory, statistical decision functions, random processes held at Liblice near Prague from November, 28 to 30, pp. 105–125, 1957.
N. Hussain, A. R. Khan, and R. P. Agarwal, Krasnoselskii and Ky Fan type fixed point theorems in ordered Banach spaces, J.Nonlinear Convex Anal., vol. 11, no. 3, pp. 475–489, 2010.
N. Hussain, S. Khaleghizadeh, P. Salimi, and F. Akbar, New fixed point results with PPF dependence in Banach spaces endowed with a graph, Abstract and Applied Analysis, vol. 2013, pp. 1-9, 2013.
N. Hussain, and M. A. Taoudi, Krasnoselskii-type fixed point theorems with applications to Volterra integral equations, Fixed Point Theory Appl., vol. 196, pp. 1–16, 2013.
N. Hussain, Lj.´Ciri´ c, and N. Shafqat, Random fixed points for Ψ-contractions with application to random differential equations, Filoma, vol. 31 no. 3, pp. 759–779, 2017.
S. Itoh, Random fixed point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl., vol. 67, pp. 261-273, 1979.
A. Kaewcharoen, PPF depended common fixed point theorems for mappings in Banach spaces, J. Inequalities Appl., vol. 2013, pp.1-14, 2013.
M. A. Kutbi, N. Hussain, and S. Khaleghizadeh, New PPF dependent fixed point theorems for Suzuki type GF-contractions, J. Function Spaces, vol. 2015, pp. 1-13, 2015.
J. J. Nieto, and R. Rodr´ıguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, vol. 22, pp. 223–239, 2005.
V. Parvaneh, H. Hosseinzadeh, N. Hussain, and Lj.´Ciri´ c, PPF dependent fixed point results for hybrid rational and Suzuki-Edelstein type contractions in Banach spaces, Filomat, vol. 30, no. 5, pp. 1339-1351, 2016.
R. A. Rashwan, and H. A. Hammad, Random fixed point theorems with an application to a random nonlinear integral equation,Journal of Linear and Topological Algebra, vol. 5, pp. 119-133, 2016.
R.A.Rashwan,and H.A.Hammad, Random common fixed point theorem for random weakly subsequentially continuous generalized contractions with application, Int. J. Pure Appl. Math., vol. 109, pp. 813-826, 2016.
P. Saipara, W. Kumam, and P. Chaipunya, Modified random errors S-iterative process for stochastic fixed point theorems in a generalized convex metric space, Stat., Optim. Inf. Comput., vol. 5, no. 1, pp65.4, 2017.
W. Sintunavarat, and P. Kumam, PPF dependent fixed point theorems for rational type contraction mappings in Banach Spaces, J.Nonlinear Anal. Optim. Theory & Appl., vol. 4, pp. 157-162, 2013.
A. Spacek, Zufallige Gleichungen, Czechoslovak Math. J., vol. 5, pp. 462-466, 1955.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).