435
Views
1
CrossRef citations to date
0
Altmetric
Article

On strongly generalized convex stochastic processes

, &
Pages 2908-2923 | Received 22 Sep 2021, Accepted 17 Nov 2022, Published online: 06 Dec 2022

References

  • Allen, L. J. 2010. An introduction to stochastic processes with applications to biology. Boca Raton, FL: CRC Press.
  • Awan, M. U., M. A. Noor, K. I. Noor, and F. Safdar. 2017. On strongly generalized convex functions. Filomat 31 (18):5783–90. doi: 10.2298/FIL1718783A.
  • Farid, G., A. U. Rehman, S. Bibi, and Y. -M. Chu. 2021. Refinements of two fractional versions of hadamard inequalities for caputo fractional derivatives and related results. Open Journal of Mathematical Science 5 (1):1–10.
  • Fu, H., M. S. Saleem, W. Nazeer, M. Ghafoor, and P. Li. 2021. On Hermite-Hadamard type inequalities for n-polynomial convex stochastic processes. AIMS Mathematics 6 (6):6322–39. doi: 10.3934/math.2021371.
  • Gonzales, L., J. Materano, and M. Lopez. 2016. Ostrowski-type inequalities via hconvex stochastic processes. JP Journal of Mathematical Sciences 16 (2):15–29.
  • Ibrahim, A. 2020. On strongly h-convex stochastic processes. Journal of Quality Measurement and Analysis JQMA 16 (2):243–51.
  • Iftikhar, M., A. Qayyum, S. Fahad, and M. Arslan. 2021. A new version of ostrowski type integral inequalities for different differentiable mapping. Open Journal of Mathematical Science 5 (1):353–9.
  • Jung, C. Y., M. S. Saleem, S. Bilal, W. Nazeer, and M. Ghafoor. 2021. Some properties of η-convex stochastic processes. AIMS Mathematics 6 (1):726–36. doi: 10.3934/math.2021044.
  • Karahan, V., and N. Okur. 2018. Hermite-Hadamard type inequalities for convex stochastic processes on n-coordinates. Turkish Journal of Mathematics and Computer Science 10:256–62.
  • Karamardian, S. 1969. The nonlinear complementarity problem with applications, part 1. Journal of Optimization Theory and Applications 4 (2):87–98. doi: 10.1007/BF00927414.
  • Kotrys, D. 2012. Hermite–Hadamard inequality for convex stochastic processes. Aequationes Mathematicae 83 (1–2):143–51. doi: 10.1007/s00010-011-0090-1.
  • Kotrys, D. 2013. Remarks on strongly convex stochastic processes. Aequationes Mathematicae 86 (1–2):91–8. doi: 10.1007/s00010-012-0163-9.
  • Kuhn, D. 2006. Generalized bounds for convex multistage stochastic programs. Vol. 548. Berlin: Springer.
  • Merentes, N., and K. Nikodem. 2010. Remarks on strongly convex functions. Aequationes Mathematicae 80 (1–2):193–9. doi: 10.1007/s00010-010-0043-0.
  • Nikodem, K. 1980. On convex stochastic processes. Aequationes Mathematicae 20 (1):184–97. doi: 10.1007/BF02190513.
  • Nikodem, K., and Z. Pales. 2011. Characterizations of inner product spaces by strongly convex functions. Banach Journal of Mathematical Analysis 5 (1):83–7. doi: 10.15352/bjma/1313362982.
  • Omaba, M., L. O. Omenyi, and L. Omenyi. 2021. Generalized fractional hadamard type inequalities for (qs)-class functions of the second kind. Open Journal of Mathematical Sciences 5(1):270–8.
  • Omaba, M. E., and E. R. Nwaeze. 2020. Generalized fractional inequalities of the Hermite–Hadamard type for convex stochastic processes. Annales Mathematicae Silesianae 35 (1):90–104. doi: 10.2478/amsil-2020-0026.
  • Özcan, S. 2019. Hermite-hadamard type inequalities for exponentially p-convex stochastic processes. Sakarya University Journal of Science 23 (5):1012–8. doi: 10.16984/saufenbilder.561040.
  • Polyak, B. T. 1966. Existence theorems and convergence of minimizing sequences in extremum problems with restrictions. Soviet Mathematics - Doklady 7:72–5.
  • Sharma, N., R. Mishra, and A. Hamdi. 2020. Hermite-Hadamard type integral inequalities for multidimensional general h-harmonic preinvex stochastic processes. Communications in Statistics-Theory and Methods 51:6719–40.
  • Sharma, N., S. K. Singh, S. K. Mishra, and A. Hamdi. 2021. Hermite–Hadamard-type inequalities for interval-valued preinvex functions via Riemann–Liouville fractional integrals. Journal of Inequalities and Applications 2021 (1):1–15. doi: 10.1186/s13660-021-02623-w.
  • Sobczyk, K. 2013. Stochastic differential equations with applications to physics and engineering. Vol. 40. Dordrecht: Springer.
  • Tariq, M., S. I. Butt, and S. Butt. 2021. Some ostrowski type integral inequalities via generalized harmonic convex functions. Open Journal of Mathematical Sciences 5 (1):200–8.
  • Tomar, M., E. Set, and N. O. Bekar. 2014. Hermite-hadamard type inequalities for strongly-log-convex stochastic processes. Journal of Global Engineering Studies 1:53–61.