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Due to the uniqueness and self-similarity, fractals became most attractive and charming research field. Nowadays researchers use different techniques to generate beautiful fractals for a complex polynomial z n + c. This article demonstrates some fixed point results for a sine function (i.e. sin(z n ) + c) via non-standard iterations (i.e. Mann, Ishikawa and Noor iterations etc.). Since each two steps iteration (i.e. Ishikawa and S iterations) or each three steps iteration (i.e. Noor, CR and SP iterations) have same escape radii for any complex polynomial, so we use these results for S, CR and SP iterations also to apply for the generation of Julia and Mandelbrot sets with sin(z n ) + c. At some fixed input parameters, we observe the engrossing behavior of Julia and Mandelbrot sets for different n.INDEX TERMS Fixed points, sine function, fractals.HENGXIAO QI was born in Shandong, China, in 1964. He received the B.Sc. degree and the master's degree in basic mathematics from the

Complex fractals achieved the highest popularity in the last ten years. Researchers used the fixed point iterations to visualize the fractals and compared the image generation times to check the efficiencies of iterations. This paper explores the behavior of Jungck-M iteration in the generation of anti-Mandelbrot sets. We define the orbit of Jungck-M iteration and prove its escape criteria. We establish the algorithm for anti-Mandelbrot set and visualize some graphs via proposed iteration. We calculate the image generation times for the generation of anti-Mandelbrot sets in proposed orbit and present the comparison with Jungck-CR iteration. We also discuss the variations in images at different values of the input parameters. Moreover, we present the graphs to show the escape time depends on input parameters.

A discrete-time Michaelis-Menten-type prey harvesting is discussed in this paper, in the modified Leslie-Gower predator-prey model. Detailed analysis of the topology of nonnegative interior fixed points is given, including their existence and stability dynamics. Also, the conditions for the existence of flip and Neimark-Sacker bifurcations are derived by using the center manifold theorem and bifurcation theory. The numerical simulations are provided, using a computer package, to illustrate the consistency of theoretical results.

In the present research, we introduce the notion of convex stochastic processes namely; strongly p-convex stochastic processes. We establish a generalized version of Ostrowski-type integral inequalities for strongly p-convex stochastic processes in the setting of a generalized k-fractional Hilfer–Katugampola derivative by using the Hölder and power-mean inequalities. By using our main results, we derived some known results as special cases and many well-known existing results are also recaptured. It is assumed that this research will offer new guidelines in fractional calculus.