s-Convex Functions in the Fourth Sense and Some of Their Properties

Year 2021, Volume: 9 Issue: 2, 260 - 267, 15.10.2021

Zeynep Eken , Sevda Sezer , Gültekin Tınaztepe , Gabil Adilov

Abstract

s-Convex functions are introduced. Its main characterizations, algebraic and
functional properties are presented. Also, some relations between these
functions and the other types of $s$-convex functions are given.

Keywords

convex function, $s$-convex function, convexity

References

• G. Adilov and I. Yesilce, $B^{-1}$-convex Functions, Journal of Convex Analysis, 24 (2)(2017), 505--517.
• G. Adilov and I. Yesilce, Some important properties of B-convex functions, Journal of Nonlinear and Convex Analysis. {19}(4) (2018), 669--680
• G. Adilov and I. Yesilce, On generalizations of the concept of convexity, Hacettepe Journal of Mathematics and Statistics. 41 (5)(2012), 723--730
• G. Adilov, G. Tınaztepe and R. Tınaztepe, On the global minimization of increasing positively homogeneous functions over the unit simplex, International Journal of Computer Mathematics. 87 (12)(2010), 2733-2746.
• M. Alomari and M. Darus, On co-ordinated s-convex functions, Int. Math. Forum. 3(40) (2008).
• K. A. Al-Hujaili, T. Y. Al-Naffouri and M. Moinuddin, (2016, March). The steady-state of the (Normalized) LMS is schur convex. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (pp. 4900-4904). IEEE.
• A. Bayoumi and A. F. Ahmed, p-Convex Functions in Discrete Sets, International Journal of Engineering and Applied Sciences. 4 (10)(2017), 63--66.
• A. Bayoumi, Foundation of complex analysis in non locally convex spaces, North Holland, Mathematics Studies. 193, Elsevier (2003).
• W. W. Breckner, Stetigkeitsaussagen f\"{u}r eine Klasse verallgemekterter konvexer Funktionen in topologischen linearen Raumen, Publ. Inst. Math. 23 (1978), 13--20.
• W. Briec and C. Horvath, $B$-convexity, Optimization. 53(2)(2004), 103--127.
• W. Briec and C. Horvath, Nash points, Ky Fan inequality and equilibria of abstract economies in Max-Plus and B-convexity. Journal of Mathematical Analysis and Applications. 341(1)(2008), 188-199.
• W. Briec, and C. Horvath, B-convex production model for evaluating performance of firms. Journal of Mathematical Analysis and Applications, 355(1) (2009), 131-144.
• S. Kemali, I. Yesilce and G. Adilov, $B$-Convexity, $B^{-1}$-Convexity, and Their Comparison, Numerical Functional Analysis and Optimization. 36(2)(2015), 133--146.
• Y. C. Kwun, M. Tanveer, W. Nazeer and K. Gdawiec, S. M. Kang, Mandelbrot and Julia Sets via Jungck--CR Iteration with \$ s\$--Convexity. IEEE Access, 7, (2019), 12167-12176.
• B. Micherda and T. Rajba, On some Hermite-Hadamard-Fej\'{e}r inequalities for (k, h)-convex functions. Math. Inequal. Appl. 15 (4)(2012), 931-940.
• J. Musielak, Orlicz spaces and modular spaces, Springer-Verlag, 2006
• M. A. Noor, K. I. Noor and T. M. Rassias, Relative strongly exponentially convex functions, Nonlinear Analysis and Global Optimization (2021) 357-371.
• G. Tınaztepe, I. Yesilce and G. Adilov, Separation of $B^{-1}$-convex Sets by $B^{-1}$-measurable Maps, Journal of Convex Analysis. 21 (2) (2014), 571--580.
• V. M. Tikhomirov, The evolution of methods of convex optimization. The American Mathematical Monthly, 103(1) (1996), 65-71.
• Z. Yao, K. Liu, S. C. Leung and K. K. Lai, Single period stochastic inventory problems with ordering or returns policies. Computers and Industrial Engineering, 61(2) (2011), 242-253.
• I. Yesilce and G. Adilov, Some Operations on $B^{-1}$ -convex Sets. Journal of Mathematical Sciences: Advances and Applications. 39 (1) (2016), 99--104.